# Differentiate $\cosh^2(2x)$

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?

• Don't forget $\sinh2y=2\sinh y\cosh y$. – Lord Shark the Unknown Apr 8 '18 at 11:59
• @LordSharktheUnknown AHhhh got it thanks:) – Unicollision Apr 8 '18 at 12:03

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.