GATE Papers >> Civil >> 2017 >> 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

• (A)  $\style{font-family:'Times New Roman'}{\frac{dw}{dx}\frac{dx}{dt}+\frac{dw}{dy}\frac{dt}{dt}}$   
• (B)  $\style{font-family:'Times New Roman'}{\frac{\partial w}{\partial x}\frac{\partial x}{\partial t}+\frac{\partial w}{\partial y}\frac{\partial y}{\partial t}}$   
• (C)  $\style{font-family:'Times New Roman'}{\frac{\partial w}{\partial x}\frac{dx}{dt}+\frac{\partial w}{\partial y}\frac{dy}{dt}}$   
• (D)  $\style{font-family:'Times New Roman'}{\frac{dw}{dx}\frac{\partial x}{\partial t}+\frac{dw}{dy}\frac{\partial y}{\partial t}}$