Find dy/dt.
-$$y = 4 t ( 5 t + 4 ) ^ { 4 }$$

Name: Find dy/dt. -\[y = 4 t ( 5 t + 4 ) ^ { 4 }\]
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Question

Quizplus · Accepted Answer

We use the chain rule to differentiate. First, we see that the derivative of the entire expression inside the parentheses is $10t + 4$. If we let $u = 5t + 4$, then $y = 4tu^4$. Thus, 
$$\frac{dy}{dt} = 4u^4 \frac{du}{dt} + 4t \cdot 4u^3 \frac{du}{dt} = 4u^3\frac{du}{dt}(5u+4) = 4(5t+4)^3 (25t+4)$$ 
which is equivalent to choice $\boxed{\textbf{(C)}}$.

Find Dy/dt y=4t(5t+4)4y = 4 t ( 5 t + 4 ) ^ { 4 }y=4t(5t+4)4

Find Dy/dt $y = 4 t ( 5 t + 4 ) ^ { 4 }$