# Math Help - What is the derivative of 1+sin^2[2x]?

1. ## What is the derivative of 1+sin^2[2x]?

derivation of $1+sin^22x$
and derivation of $\frac{1}{3}-cot^32x$

Can you show me how did you get the answer?

2. Think of this as f = 1 + u^2 where u = sin(2x)
By the chain rule

df/dx =df/du*du/dx = 2u du/dx = 2sin(2x)*cos(2x)*2

Similar think of this as 1 - u^3 = cot(2x)

go from here

3. Originally Posted by Yuroichi
derivation of $1+\sin^{2}2x$

Can you show me how did you get the answer?
$\begin{gathered}\frac{d}{{dx}}\left( {1 + {{\sin }^2}2x} \right) = 2\sin 2x \cdot \frac{d}{{dx}}\left( {\sin 2x} \right) = \hfill \\= 2\sin 2x\cos 2x \cdot \frac{d}{{dx}}\left( {2x} \right) = 4\sin 2x\cos 2x = 2\sin 4x. \hfill \\\end{gathered}$