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

1. $3x^{2}y+1, \: x^{3}+1$
2. $3x^{2}y+e^{x}, \: x^{3}$
3. $x^{3}y+xe^{x}, \: x^{3}+e^{x}$
4. $2x^{2}y+\dfrac{e^{x}}{x}$

option B will be correct.

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

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