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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. $2x^{2}y+\dfrac{e^{x}}{x}$
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2 Answers

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option B will be correct.

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

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