Sunday, December 29, 2019

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 68

Find a.) F(x) and b.) G(x) where F(x)=f(xα and G(x)=[f(x)α]. Suppose that f is differentiable everywhere and α is a real number.


 a.) F(x)=ddx[f(x)]=f(xα)α(xα1)F(x)=ddx[f(x)]=αxα1f(xα) b.) G(x)=ddx[G(x)]=α[f(x)]α1f(x)1G(x)=ddx[G(x)]=α[f(x)]α1f(x)1G(x)=ddx[G(x)]=α[f(x)]α1f(x)

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