$\"\"$

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The function is $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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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

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differentiable at $\"\"$ and $\"\"$ .

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Find $\"\"$ .

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Equate the function to $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ in above equation.

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$\"\"$

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$\"\"$ is clearly root of the equation.

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

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$\"\"$

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Consider $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$ .

\

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Power rule of derivatives : $\"\"$ .

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$\"\"$

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From theorem 7, $\"\"$ .

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Substitute $\"\"$ in above equation.

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .