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(xα−1)F′(x)=ddx[f(x)]=αxα−1f′(xα) b.) G′(x)=ddx[G(x)]=α[f(x)]α−1⋅f′(x)⋅1G′(x)=ddx[G(x)]=α[f(x)]α−1⋅f′(x)⋅1G′(x)=ddx[G(x)]=α[f(x)]α−1f′(x)
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