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If f (1) = 4; f ′ (1) = 2, find the value of the derivative of log f(ex) w.r.t x at the point x = 0.

If f (1) = 4; f ′ (1) = 2, find the value of the derivative of log f(ex) w.r.t x at the point x = 0.

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1 Answers

Ravi
askIITians Faculty 69 Points
9 years ago
Let g(x)=log f(ex)
so, g’(x)=[1/f(ex)][f’(ex)]
Applying chain rule, We get

\frac{d}{dx} g(x)=\frac{1}{f(e^{x})}\frac{d}{dx} f(e^{x})

\frac{d}{dx} g(0)=\frac{1}{f(1)}\ f'(1)
Now, put the values to obtain the answer.

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