Question $9$

Use the inverse function theorem to find the derivative of $g(x)=\sqrt[4]{x}.$

$g^{\text{'}}(x)=\frac{1}{f^{\text{'}}(g(x))},$ where $f(x)=g^{-1}(x)$

Step $1f(x)=g^{-1}(x)=$

Step $2,f^{\text{'}}(x)=$

Step $3,f^{\text{'}}(g(x))=$

Step $4,\frac{1}{f^{\text{'}}(g(x))}=$

Now, find $g^{\text{'}}(x)$ by differntiating $g(x)$ using the power rule, since $\sqrt[4]{x}=x^{\frac{1}{4}}.$

$g^{\text{'}}(x)=$

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$\frac{0}{1}$ pt