4 years ago

Find the derivative of the inverse function of the original function f(x)=(x+1)^3-5

Mathematics

1 answer:

____ [38]4 years ago

4 0

Answer:

Step-by-step explanation:

let f(x)=y

$y=(x+1)^{3} -5\\flip ~x~and~y\\x=(y+1)^{3}-5\\(y+1)^{3}=x+5\\y=(x+5)^{\frac{1}{3} } -1\\or~f^{-1}(x)=(x+5)^{\frac{1}{3} } -1\\(f^{-1})'(x)=\frac{1}{3} (x+5)^{\frac{-2}{3} }$

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