Differentiate $\cosh^2(2x)$

Question

I know I can differentiate directly and get the answer $2\cosh(2x)\cdot2\sinh(2x)$ which equals to $4\cosh(2x)\sinh(2x)$.

But when I attempted the question, I tried to convert $\cosh^2(2x)$ into $\frac{\cosh(4x)+1}2$, using the identity $\cosh(2x)=2\cosh^2(x)-1$. After the conversion, the answer I get differentiating this will be $2\sinh(4x)$ which is a different answer?

Can someone please explain where went wrong?

Answer 1

Do not worry, your answers are identical.

Note that $$4\cosh(2x)\sinh(2x)= 2\sinh(4x)$$

because we have a formula $$ \sinh(2x)=2\sinh(x)\cosh(x)$$

Upon substitution of $2x$ for $x$ you get your two answers identical.