Calculus Archive: Questions from July 11, 2023
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Calculate the directional derivative of the function at the given point in the direction of the vector u.
Calcule la derivada direccional de la función en el punto dado en la dirección del vector \( u \). \[ \begin{array}{l} h(x, y, z)=\cos x y+e^{y z}+\ln z x, \quad P_{0}(1,0,1 / 2) \\ \mathbf{u}=\math2 answers -
Given \( f(x, y)=x^{2} y^{3}+10 \ln (y) \), then \( \frac{\partial f}{\partial y}= \) Given \( g(x, y, z)=\frac{x \tan (y)}{z} \), then \( g_{z}= \)2 answers -
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Find and graph the image of \( D=\left\{(x, y) \in \mathbb{R}^{2} \mid 0 \leq x \leq 2,1 \leq y \leq 4\right\} \) under \( T(x, y)=(6 x-4 y, 2 x+y) \)2 answers -
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\[ y=\sin ^{-1}(\sqrt{3 x}+1) \] b) \( y=\cos ^{3}\left(5 x^{2}+1\right) \) c) \( 7 x+2 y+\sin (x y)=8 \)2 answers -
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