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Product Rule and Chain Rule Calculations

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I have done most of the calculations but require confirmation.

a) Use the product rule to show that if m is a positive integer then,

b) By applying the product rule and the chain rule of differentiation to the functions and derive the quotient rule.
That is, show that

Assume that for any

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The expert examines product rules and chain rule calculations.

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Hi. Since much of the question involves integration I'll write it out in formatted form in the attached PDF file also.

a.) For m>0, x^m is differentiable and its derivative mx^{m-1} does not take the value zero. ...

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