NIELIT 2016 MAR Scientist C - Section B: 5

Question

If $f(x,y)=x^{3}y+e^{x},$ the partial derivatives, $\dfrac{\partial f}{\partial x},\dfrac{\partial f}{\partial y}$ are

• A. $3x^{2}y+1, \: x^{3}+1$
• B. $3x^{2}y+e^{x}, \: x^{3}$
• C. $x^{3}y+xe^{x}, \: x^{3}+e^{x}$
• D. $2x^{2}y+\dfrac{e^{x}}{x}$

Answer 1

option B will be correct.

while partially differentianting with respect to x, y is considered as constant. and vice-versa

Answer 2

option B is correct.