Find a formula for the derivative of the following functions. 3. y=3e10x+4x4 4. f(x)=4e2x2−x 5. y=ln(4x3)+e5x 6. y=ln(3x2−5x)5. y=ln(4x3)+e5x 6. y=ln(3x2−5x) 7. y=(3e2x−4)4

3) Given y=3e^(10x)+4x^4 we have to find the derivative of y,dy/dx since we know that d/dx(x^n)=nx^(n-1),d/dx(e^(ax))=ae^(ax)

Resuelto Find a formula for the derivative of the following

Nuestra ayuda de expertos desglosó tu problema en una solución confiable y fácil de entender.

Pregunta: Find a formula for the derivative of the following functions. 3. y=3e10x+4x4 4. f(x)=4e2x2−x 5. y=ln(4x3)+e5x 6. y=ln(3x2−5x)5. y=ln(4x3)+e5x 6. y=ln(3x2−5x) 7. y=(3e2x−4)4

Muestra el texto de la transcripción de la imagen
Hay 4 pasos para resolver este problema.
Solución
Paso 1
$3)$ Given $y = 3 e^{10 x} + 4 x^{4}$
we have to find the derivative of $y, \frac{d y}{d x}$
$\begin{matrix} \begin{aligned} y & = 3 e^{10 x} + 4 x^{4} \\ \frac{d y}{d x} & = \frac{d}{d x} (3 e^{10 x} + 4 x^{4}) \\ = 3 \frac{d}{d x} (e^{10 x}) + 4 \frac{d}{d x} (x^{4}) \\ = 3 (e^{10 x}) \frac{d}{d x} (10 x) + 4 (4 x^{3}) \\ = 3 (10) e^{10 x} (1) + 16 x^{3} \\ = 30 e^{10 x} + 16 x^{3} \end{aligned} \end{matrix}$

Explanation:
since we know that $\frac{d}{d x} (x^{n}) = n x^{n - 1}, \frac{d}{d x} (e^{a x}) = a e^{a x}$
Mira la respuesta completa
Paso 2
Desbloquea
Paso 3
Desbloquea
Paso 4
Desbloquea
Respuesta
Desbloquea