To show: The derivative of the inverse function .
The function is one to one and differentiable and its inverse also differentiable.
Obtain the derivative of the function .
Since the function is one to one function, .
Differentiate implicitly with respect to x.
Apply the chain rule and simplify the terms,
Divided by on both sides,
Hence the required result is proved.
To find: The value .
The value of is .
Obtain the value of .
From part (a), .
Substitute 5 for x,
Since the function is one to one, implies that .
Substitute and ,
Therefore, the value of is .
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