Question

y = cot2(sin θ)


derivitive?

Answer 1

and y = sin(tan 5x)

Answer 2

Okay let \(u=\sin\theta\).\[
y=\cot^2(u)
\]Now let \(v = \cot(u)\)\[
y=v^2
\]

Answer 3

\[
\frac{dy}{d\theta }=\frac{dy}{dv}\frac{dv}{d\theta}=\frac{dy}{dv}\frac{dv}{du}\frac{du}{d\theta }
\]

Answer 4

\[\begin{split}
\frac{dy}{d\theta}
&=(2v)(-\csc^2(u))(\cos(\theta) )&v=\cot(u)\\
&=(2\cot (u))(-\csc^2(u))(\cos(\theta) )&u=\sin(\theta) \\
&=(2\cot (\sin\theta ))(-\csc^2(\sin \theta ))(\cos(\theta) )

\end{split}
\]

Answer 5

Chain rule can get a bit messy.