Nested derivatives and increasing intervals

(a) Suppose the following facts are known about the function gg and its derivative: g(5)=1g(5)=1, g′(5)=−3g'(5)=-3. If f(x)=tan⁡(eg(x))f(x)=\tan(e^{g(x)}), find the value of f′(5)f'(5). marks

(b) Find, by differentiation, the range of values of xx for which the function y=x22x−1y=\frac{x^2}{2x-1} increases as xx increases. marks

[2009/DHS/Prelim/I/4]

Total marks: 6

Solution

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  1. (a) Chain rule →
  2. (b) Increasing functions →