Question

como resolver esta derivada e simplificar caso precise f(x)=(x^2+1)^5/(2x+3)^6

Answer 1

Boa tarde! 

Solução!

Derivada do quociente!

$\left ( \dfrac{u}{v}\right )' =\left (\dfrac{(v \times u')-(u \times v')}{v^{2} }\right )$



$u=( x^{2} +1)^{5} ~~~~~~~~~v=(2x+3)^{6}\\\\\\\\ u'=10x( x^{2} +1)^{4} ~~~~~~~~~v'=12(2x+3)^{5}$


$\left (\dfrac{(2x+3)^{6} \times10x( x^{2} +1)^{4}-(x^{2} +1)^{5} \times12(2x+3)^{5} }{((2x+3)^{6})^{2} }\right )\\\\\\\\\\ \left (\dfrac{(2x+3)^{6} \times10x( x^{2} +1)^{4}-(x^{2} +1)^{5} \times12(2x+3)^{5} }{(2x+3)^{12} }\right )$


Boa tarde!
Bons estudos!