# GATE Papers >> Civil >> 2017 >> Question No 102

Question No. 102

let $\style{font-family:'Times New Roman'}{w=f(x,\;y),}$ where $x$ and $y$ are function of $t$. Then according to the chain rule, $\style{font-family:'Times New Roman'}{\frac{dw}{dt}}$ is equal to

##### Answer : (C) $\style{font-family:'Times New Roman'}{\frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt}}$

Solution of Question No 102 of GATE 2017 Civil Paper

w = f (x, y)

$\frac{\mathrm{dw}}{\mathrm{dt}}=\frac{\partial\mathrm w}{\partial\mathrm x}\frac{\mathrm{dx}}{\mathrm{dt}}+\frac{\partial\mathrm w}{\partial\mathrm y}\frac{\mathrm{dy}}{\mathrm{dt}}$