Question

Sendo f(x)=x^3-8,a derivada da função inversa de f,ou seja,f(-1)

Answer 1

$f(x)= x^{3} -8,achar,aderivada,da,inversa,de,f(x) \\ achar a f(x)_{-1} \\ x= f(x)_{-1} ^{3}-8 \\ f(x)_{-1} ^{3}=x+8 \\ f(x)_{-1}= \sqrt[3]{x+8} \\ f(x)'_{-1}= \frac{1}{3}. \frac{1}{ \sqrt[3]{ ( \\ x+8)^{2} } } \\ f(x)'_{-1}= \frac{1}{3. \sqrt[3]{ (x+8)^{2} } }$