Question

Derivative of (2x+5)^4(5x+2)^-2

Answer 1

Use chain rule

$\frac{d}{dx}f(x)g(x)=f'(x)g(x)+g'(x)f(x)$

and also power rule
$\frac{d}{dx} x^m=mx^{m-1}$

so

well, we will say $f(x)=(2x+5)^4$ and $g(x)=(5x+2)^{-2}$
$f'(x)=4(2x+5)^3(\frac{d}{dy}(2x+5))=4(2x+5)^3(2)=8(2x+5)^3$
$g'(x)=-2(5x+2)^{-3}(\frac{d}{dx}(5x+2))=-2(5x+2)^{-3}(5)=-10(5x+2)^{-3}$


so
$\frac{d}{dx}(2x+5)^4(5x+2)^{-2}=8(2x+5)^3(5x+2)^{-2}+(-10(5x+2)^{-3})(2x+5)^4)$
simplify yourself