Question

Use the Chain Rule to find dw/dt. w = xey/z, x = t3, y = 7 − t, z = 8 + 4t dw dt =

Answer 1

$\frac{dw}{dt} = \frac{dx}{dt} \times \frac{dw}{dx} + \frac{dy}{dt} \times \frac{dw}{dy} + \frac{dz}{dt} \times \frac{dw}{dz} \\ \frac{dw}{dt} = 3t ^{2} \times {e}^{ \frac{y}{z} } + - t \times \frac{x {e}^{ \frac{y}{z} } }{z} + 4 \times - \frac{xy {e}^{ \frac{y}{z} } }{ {z}^{2} } \\ \frac{dw}{dt} = \frac{ {e}^{ \frac{y}{z} } (3 {t}^{2} {z}^{2} - tzx - 4xy)}{ {z}^{2} }$