$$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$$
-$$y = \sin e ^ { - \theta ^ { 7 } }$$
A) $\cos e ^ { - \theta ^ { 7 } }$
B) $\cos \left( - 7 \theta ^ { 6 } \mathrm { e } ^ { - \theta ^ { 7 } } \right)$
C) $7 \theta ^ { 6 } \cos \mathrm { e } ^ { - \theta ^ { 7 } }$
D) $\left( - 7 \theta ^ { 6 } \mathrm { e } ^ { - \theta ^ { 7 } } \right) \cos \mathrm { e } ^ { - \theta ^ { 7 } }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = \sin e ^ { - \theta ^ { 7 } }$ with respect to $\theta$, we use the chain rule. First, differentiate the outer function ($\sin$) with respect to its inner function ($e ^ { - \theta ^ { 7 } }$), which gives $\cos e ^ { - \theta ^ { 7 } }$. Then, differentiate the inner function ($e ^ { - \theta ^ { 7 } }$) with respect to $\theta$, which gives $-7\theta^6 e^{-\theta^7}$. Multiply these two derivatives together to get the final answer: $\left( - 7 \theta ^ { 6 } \mathrm { e } ^ { - \theta ^ { 7 } } \right) \cos \mathrm { e } ^ { - \theta ^ { 7 } }$.

Find the derivative of y with respect to x,t, or θ, as appropriate. \text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. } Find the derivative of y with respect to x,t, or θ, as appropriate.

$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$