$\"\"$

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The function is $\"\"$ .

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Find $\"\"$ when $\"\"$ is the inverse of the function $\"\"$ .

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Theorem 7 :

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If $\"\"$ is a one to one differentiable function with inverse function $\"\"$ and $\"\"$ then the inverse function is differentiable at $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in the function.

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$\"\"$

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Therefore $\"\"$ then $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ then $\"\"$ .

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$\"\"$

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$\"\"$ is the inverse function of $\"\"$ then $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$ .