Question

derivada de f(x)=1/3(2x^5+6x^-3)^5
Resposta 10/3 (2x^5+6x^-3)^4(5x^4-9x^-4)

Answer 1

$Regra\ do\ Produto\ e\ Regra\ da\ Cadeia\\\\f'(x)=g'(x)\cdot{h(x)}+g'(x)\cdot{h'(x)}\\\\g(x)= \dfrac{1}{3}\ ......\ g'(x)=0\\\\\\h(x)=(2x^5+6x^{-3})^5\\\\h'(x)=u'(x)\cdot{h'(u)}\\h(u)=u^5\ ...... \ h'(u)=5u^4\\\\u(x)=2x^5+6x^{-3}\\u'(x)=10x^4-18x^{-4}\\\\h'(x)=(10x^4-18x^{-4})\cdot{5(2x^5+6x^{-3})^4$

$f'(x)= \dfrac{1}{3}(10x^4-18x^{-4})\cdot5(2x^5+6x^{-3})^4\\\\\\f'(x)= \dfrac{10}{3}(5x^4-9x^{-4})\cdot(2x^5+6x^{-3})^4$