Derivative of cos(e^-θ^2) using the chain rule | Power and exponential rules

[jaydnul]

Homework Statement

Find the derivative of the following

cos(e^-θ^2)

Homework Equations

cos=-sin
e^x=e^x
power rule

The Attempt at a Solution

So I have gotten this far: -sin(e^-θ^2) * ... but then i don't know where to go. Would I treat the -θ^2 as the next step inwards? My best guess would be this:

-sin(e^-θ^2) * e^-2θ * e^-θ^2

 

[MostlyHarmless]

This is chain rule inside of the chain rule.

So, {\cos(e^{-θ^2})} let u=e^{-θ^2} to find du, letv=-θ^2dv=-2θd{\theta} so du=-2θe^{-θ^2}d{\theta} and finally {\frac{d({cos(u)})}{du}=-{sin(u)}du}

 

[jaydnul]

Perfect