Calculus Archive: Questions from October 04, 2023
-
1 answer
-
Differentiate the following function. \[ \begin{array}{l} y=\left(x^{4}+3 x\right)^{12} \\ y^{\prime}=12\left(x^{4}+3 x\right)^{11}\left(4 x^{3}+3\right) \\ y^{\prime}=12\left(x^{4}+3 x\right)^{13}\le1 answer -
Differentiate the following function. \[ y=\left(x^{8}+9\right)(6 x-7)^{5} \] \[ \begin{array}{l} y^{\prime}=\left(8 x^{7}\right)(6 x-7)^{5}-\left(x^{8}+9\right)(5)(6 x-7)^{4} \\ y^{\prime}=\left(8 x^1 answer -
Differentiate the following function. \[ y=\frac{(6 x-7)^{5}}{x^{3}} \] \[ \begin{array}{l} y^{\prime}=\frac{5(6 x-7)^{4}(6) x^{3}-(6 x-7)^{5} 3 x^{2}}{x^{6}} \\ y^{\prime}=\frac{5(6 x-7)^{4} x^{3}-(61 answer -
Given \[ z=x^{3}+x y^{2}, x=u v^{3}+w^{5}, \quad y=u+v e^{w} \] then find: \( \frac{\partial z}{\partial w} \) when \( u=-1, v=1, w=0 \)1 answer -
[9-10] Identify which of the twelve basic functions listed below fit the description given. \[ y=x, y=x^{2}, y=x^{3}, y=|x|, y=\frac{1}{x}, y=e^{x}, y=\sqrt{x}, y=\ln x, y=\sin x, y=\cos x, y=\operato1 answer -
In Exercises 5-12, find and sketch the domain for each function. 5. \( f(x, y)=\sqrt{y-x-2} \) 6. \( f(x, y)=\ln \left(x^{2}+y^{2}-4\right) \) 7. \( f(x, y)=\frac{(x-1)(y+2)}{(y-x)\left(y-x^{3}\right)1 answer -
I want to solve these questions
2) Solve the given DE: (i) \( y^{\prime \prime}+2 y^{\prime}-24 y=e^{3 x} \) (ii) \( \mathrm{y}^{\prime \prime}+4 \mathrm{y}^{\prime}+5 \mathrm{y}=35 \mathrm{e}^{-4 \mathrm{x}}, \quad \mathrm{y}(0)=-31 answer -
0 answers
-
Given \( f(x, y)=4 x^{3}+2 x^{2} y^{4}-3 y^{6} \), \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)=( \] \[ f_{x y}(x, y)=( \]1 answer -
Given \( f(x, y)=4 x^{3}+2 x^{2} y^{4}-3 y^{6} \), \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)=( \] \[ f_{x y}(x, y)=( \]1 answer -
1 answer
-
Explica la simplificación de la derivada
Despejar la derivada \( \mathrm{y}^{\prime} \) De lo hecho anteriormente tenemos \[ \mathrm{y}^{\prime}=\mathrm{y}\left(\frac{\sec ^{2} \theta}{\tan \theta}+\frac{1}{2 \theta+1}\right) \] como hemos t1 answer -
C. d dx x3-6x²+8x x²-2x ²+8x)
c. \( \quad \frac{d}{d x}\left(\frac{x^{3}-6 x^{2}+8 x}{x^{2}-2 x}\right) \)1 answer -
y = In 2x, y = 1, y = 5, x = 0 Find the volume V of this solid.
\[ y=\ln 2 x, y=1, y=5, x=0 \] Find the volume \( V \) of this solid.0 answers -
Find \( y^{\prime} \) if \( y=\ln \left(x^{2}+3\right)^{3 / 2} \) \[ y^{\prime}=\frac{\left(3 x \sqrt{\ln \left(x^{2}+3\right)}\right)}{x^{2}+3} \]2 answers -
\( (\mathrm{M} \& \mathrm{~T}, \# \) 2.3.1) Find \( \partial f / \partial x, \partial f / \partial y \) if - \( f(x, y)=x y \) - \( f(x, y)=e^{x y} \) - \( f(x, y)=x \cos x \cos y \) - \( f(x, y)=\lef1 answer -
1 answer
-
7. Solve the initial-value problem \[ \left\{\begin{array}{l} y^{\prime}=\frac{3+2 x^{2}}{x^{2}} \\ y(-2)=1 \end{array}\right. \]1 answer -
1 answer
-
Obtenga Dy/dx si x^x + y^x = 1 las fotos son solo ejemplos de lo que se ha hecho
2 da forma derivación logáritmica \[ \begin{array}{l} \ln y=\ln \left(x^{x}\right) \\ \ln y=x \ln x \\ \frac{1}{y} \cdot \frac{d y}{d x}=\frac{x}{1} \cdot \frac{1}{x}+\ln x \quad \text { (con deriva1 answer -
Find \( \frac{d y}{d x} \) when \[ -3 \sin x \sin y=-1 . \] 1. \( \frac{d y}{d x}=-3 \tan x \cot y \) 2. \( \frac{d y}{d x}=3 \tan x \cot y \) 3. \( \frac{d y}{d x}=-\cot x \tan y \) 4. \( \frac{d y}{1 answer -
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Find the total differential. \[ \begin{array}{c} z=e^{-x} \tan (y) \\ d z=-e^{-x} \tan (y)+e^{-x} \sec ^{2}(y) \end{array} \]1 answer -
Let \( f(x, y, z)=6 x y \sin (4 z)-6 y z \sin (4 x) \). Find \( f_{x}(x, y, z), f_{y}(x, y, z) \), and \( f_{z}(x, y, z) \). (Use symbolic notation and fractions where needed.) \[ f_{x}(x, y, z)= \]1 answer -
Evaluate the double integral. \[ \iint_{D} 9 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 1,0 \leq x \leq y \]1 answer -
0 answers
-
1 answer
-
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=\cos (\sin (9 \theta)) \] \[ y^{\prime}= \] \[ y^{\prime \prime}= \]1 answer -
2. Halle el valor exacto de cada expresión sin usar la calculadora. (a) \( \operatorname{sen}\left(45^{\circ}\right) \tan \left(60^{\circ}\right)+\csc \left(60^{\circ}\right) \) (b) \( 2 \operatornam1 answer -
Solve: given:
\( \frac{d \theta}{d T}=\frac{(1+\alpha(1-\cos \theta))^{2}}{\alpha \cdot h v \cdot \sin \theta} \) \( T=\frac{h v \cdot \alpha(1-\cos \theta)}{1+\alpha \cdot(1-\cos \theta)} \)1 answer -
6. Suponga que un modelo matemático de la temperatura Fahrenheit a las \( t \) horas después de medianoche, en cierto día de la semana está dado por \[ T(t)=55+10 \operatorname{sen}\left(\frac{\pi1 answer -
1 answer
-
\( \begin{array}{c}\int x^{3} \sqrt{x^{2}-36} d x \\ \frac{2592}{3} \tan ^{3}\left(\sec ^{-1}\left(\frac{x}{6}\right)\right)+\frac{7776}{5} \tan ^{5}\left(\sec ^{-1}\left(\frac{x}{6}\right)\right)+C\e1 answer -
1 answer
-
I. Determine la derivada: 1) f(x) = arctan (²x) arcsen (3x) 2) y= 3) Determine la ecaución de la línea que para tangente a la curva 1 T y=2arcsen (x) en el punto 2 3 X
I. Determine la derivada: 1) \( f(x)=\arctan \left(e^{2 x}\right) \) 2) \( y=\frac{\operatorname{arcsen}(3 x)}{x} \) 3) Determine la ecaución de la línea que para tangente a la curva \( y=2 \operato1 answer -
II. Trabaje los integrales: 1 1) S 2 x√/1-(Inx) ² √2 2) 3) 0 2 S² 0 1 4-x² 1 x²2x+2 dx dx dx
II. Trabaje los integrales: 1) \( \int \frac{1}{x \sqrt{1-(\ln x)^{2}}} d x \) 2) \( \int_{0}^{\sqrt{2}} \frac{1}{\sqrt{4-x^{2}}} d x \) 3) \( \int_{0}^{2} \frac{1}{x^{2}-2 x+2} d x \)1 answer -
1 answer
-
(1 point) Let \( f(x, y, z)=\frac{x^{2}-6 y^{2}}{y^{2}+5 z^{2}} \). Then \[ \begin{array}{l} f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]1 answer -
1 answer
-
Find \( y^{\prime}=\frac{d y}{d x} \) using implicit differentiation. \[ e^{x} \sin (y)+7 e^{y} \cos (x)=7 \]1 answer -
10. Find \( d y / d x \) for the following expression: \[ y=e^{-x} \cos 2 x \] A. \( -e^{-x}(\cos 2 x+2 \sin 2 x) \) B. \( e^{-x}(\cos 2 x+2 \sin 2 x) \) C. \( -e^{-x}(\cos 2 x-2 \sin 2 x) \) D. \( e^1 answer -
Find a Derivative
61. \( y=\frac{x}{2}-\frac{\sin 2 x}{4} \) 63. \( y=x(6 x+1)^{5} \) 65. \( f(x)=\left(\frac{x}{\sqrt{x+5}}\right)^{3} \)1 answer -
2. Solve the Initial Value Problems. a) \( y^{\prime \prime}-y^{\prime}-6 y=0, \quad y(0)=0, y^{\prime}(0)=1 \) b) \( y^{\prime \prime}-4 y=0, \quad y(0)=1, \quad y^{\prime}(0)=2 \).1 answer -
number 7!!
3-16 = Find \( d y / d x \) by implicit differentiation. 3. \( x^{3}+y^{3}=1 \) 4. \( 2 x^{3}+x^{2} y-x y^{3}=2 \) 5. \( x^{2}+x y-y^{2}=4 \) 6. \( y^{5}+x^{2} y^{3}=1+x^{4} y \) 7. \( y \cos x=x^{2}+1 answer -
please help me
\( y=\left(e^{\sqrt{x}}+\cos \left(e^{x}\right)^{3}\right. \) \( y=\frac{\left(e^{\sqrt{x}}+\cos \left(e^{x}\right)^{3}\right.}{\sqrt{x-4}} \)0 answers -
Compute the following derivative. [1²(i + 5j - 5tk) • (e'i + 5e¹j – 2e¯ 'k)] [t²(i + 5j − 5tk) • (e¹i + 5e¹j – 2e¯¹k)] = [] ***
Compute the following derivative. \[ \frac{d}{d t}\left[t^{2}(i+5 j-5 t k) \cdot\left(e^{t} \mathbf{i}+5 e^{t} j-2 e^{-t} k\right)\right] \] \[ \frac{d}{d t}\left[t^{2}(i+5 j-5 t k) \cdot\left(e^{t} i1 answer -
1 answer
-
Find the relative extrema of the function, if they exist.
\( y=1-x^{3} \) \( y=2-3 x-2 x^{2} \) \( y=\frac{5}{x^{2}+1} \)1 answer -
1 answer
-
1 answer
-
(1 point) Find \( y \) as a function of \( x \) if \[ \begin{array}{l} y^{\prime \prime \prime}-4 y^{\prime \prime}+y^{\prime}-4 y=0, \\ y(0)=0, y^{\prime}(0)=1, \quad y^{\prime \prime}(0)=-60 . \\ y(1 answer -
1 answer
-
1. \( f(x)=x^{5}+x^{4}+x^{3}+x^{2}+x+1 \) 2. \( f(x)=3 x^{7}-x^{-3 / 4}+\sqrt{x}-\frac{x^{4}}{2}+\frac{2}{x^{4}} \) 3. \( y=\left(x^{2}+x^{5}-2\right)\left(9 x^{2}-x\right) \) 4. \( g(x)=\frac{x^{2}-21 answer -
1 answer
-
1 answer
-
Integrate. \[ \begin{array}{l} \int \cos (5 x) e^{29 \sin (5 x)} d x \\ \int \cos (5 x) e^{29 \sin (5 x)} d x=+C \end{array} \]1 answer -
Given \( f(x, y)=2 x^{3} \cos \left(y^{8}\right) \) \[ \begin{array}{l} f_{x y}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
(2) (M\&T, \# 2.3.1) Find \( \partial f / \partial x, \partial f / \partial y \) if - \( f(x, y)=x y \) - \( f(x, y)=e^{x y} \) - \( f(x, y)=x \cos x \cos y \) - \( f(x, y)=\left(x^{2}+y^{2}\right) \l1 answer -
1 answer
-
Differentiate the function. y =(2x-1)^5 (3-x^4)^3 y'=
Differentiate the function. \[ y=(2 x-1)^{5}\left(3-x^{4}\right)^{3} \] \[ y^{\prime}= \]1 answer -
Resolver la siguiente ecuación diferencial usando el método analitico de ecuaciones lineales. \[ \frac{d y}{d x}-x y=x^{2} e^{x^{2} / 2}, y(0)=1.3 \] En el procedimiento deben estar todos los pasos,1 answer -
Pregunta 6 Resuelva la siguiente ecuación diferencial (x + 1) dy + (x + 2)y = 2xe¯ª En el procedimiento deben estar todos los pasos, desde identificar si es lineal y escribirla en su forma estánda
Resuelva la siguiente ecuación diferencial \[ (x+1) \frac{d y}{d x}+(x+2) y=2 x e^{-x} \] En el procedimiento deben estar todos los pasos, desde identificar si es lineal y escribirla en su forma est1 answer -
13 PLEASE THANK YOU:) Skills Practice For Problems 1-18, find dy dx 1. y = 12u - 7 and u = 3x + 1 3. y = 10u + 1 and u = -x² + 3 5. y = 3u² + 2 and u = 5x² + 4 7. y=u³- 6u and u = 5x²-2 9. y = (
For Problems 1-18, find \( \frac{d y}{d x} \). 1. \( y=12 u-7 \) and \( u=3 x+1 \) 2. \( y=16 u^{2}+u-3 \) and \( u=8 x-5 \) 3. \( y=10 u+1 \) and \( u=-x^{2}+3 \) 4. \( y=8 u-6 \) and \( u=-x^{4}+3 x1 answer -
1 answer
-
1 answer
-
need help with 2, 3 and 4 need 2, 3, 4
Determine los puntos críticos de la función y utilice los criterios estudiados para clasificarlo(s) como un máximo, mínimo o punto de silla. 1) \( f(x, y)=2 x y-\frac{1}{2}\left(x^{4}+y^{4}\right)1 answer -
need 2 and 3 and 4
Determine los puntos críticos de la función y utilice los criterios estudiados para clasificarlo(s) como un máximo, mínimo o punto de silla 1) \( f(x, y)=2 x y-\frac{1}{2}\left(x^{4}+y^{4}\right)+1 answer