Question

Find the derivative of:

f(x)=4x*3coth*2(x*2+2)

Answer 1

\[\frac{d}{dx}\coth x=-\frac{1}{\sinh^2x}\]

Answer 2

\[\frac{d}{dx}(4x^3 \ \coth^2(x^2+2))=12x^2 \coth^2(x^2+2)+4x^3(-4x \frac{\coth(x^2+2)}{\sinh^2(x^2+2)})\]

Answer 3

this may be helpful
\[\frac{d}{dx} (f^n(g(x))=n g'(x) f'(g(x)) f^{n-1}(g(x)) \]