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I've submitted a homework assignment online where it is then marked by a program and a score is instantly given back.

I was 100% correct in all solutions besides this one.

Use the Chain Rule to find $\displaystyle \frac{dw}{dt}$. $$ w = xe^{\frac{y}{z}},\,\,\, x = t^5, \,\,\, y = 4 − t, \,\,\, z = 2 + 4t $$ $$ \frac{dw}{dt} = e^{\frac{y}{z}}(5t^4) - \frac{xe^{\frac{y}{z}}}{z} $$

Can someone tell me where I've gone wrong? Apologies for the lack of formatting.

J126
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user100299
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1 Answers1

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You are using the chain rule that says: $$ \frac{dw}{dt} = \frac{\partial w}{\partial x}\frac{dx}{dt} + \frac{\partial w}{\partial y}\frac{dy}{dt} + \frac{\partial w}{\partial z}\frac{dz}{dt}. $$ Here it looks like you forgot $$\frac{\partial w}{\partial z}\frac{dz}{dt}. $$

Thomas
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