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, let$$v=-θ^2$$$$dv=-2θd{\theta}$$ so $$du=-2θe^{-θ^2}d{\theta}$$ and finally $${\frac{d({cos(u)})}{du}=-{sin(u)}du}$$

 

[jaydnul]

Perfect