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GATE 2020 EC – Question 13

Engineering Mathematics · Calculus · 1 mark · Multiple choice

The partial derivative of the function

$$f(x,y,z)=e^{1-x\cos y}+xze^{-1/(1+y^2)}$$

with respect to $x$ at the point $(1,0,e)$ is

  1. $-1$
  2. $0$
  3. $1$
  4. $\frac1e$

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Show answer and explanation

Correct answer: (B) $0$

Explanation

$\frac{\partial f}{\partial x}=-\cos y\,e^{1-x\cos y}+z\,e^{-1/(1+y^2)}$. At $(1,0,e)$: $-1\cdot e^{0}+e\cdot e^{-1}=-1+1=0$.