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A function f : R rarr R satisfies the eq...

A function `f : R rarr R` satisfies the equation `f(x + y) = f(x).f(y)` for all x, y in R and f(x) `ne` 0 for any x in R. Let the function be differentiable at x = 0 and f'(0) = 2 Show that f'(x) = 2 f(x) for all x in R. Hence, determine f(x).

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. If f(x) = e^x, find f' (3) starting from defination

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  2. If f(x) = e^(sqrtx) find f' (x) .

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  3. A function f : R rarr R satisfies the equation f(x + y) = f(x).f(y) fo...

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  4. If f(x) = log (2x-1), find f'( c ) .

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  5. If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(e^(1//x)+e^(-1//x)))",",x ne 0...

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  6. Find f'(X) using first prinicples when f(x) =e^(3x -2)

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  7. Find f'(X) using first prinicples when f(x) = log(2x +3)

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  8. Find derivative of each of the following functions: e^x + log x

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  9. Find derivative of each of the following functions: x^2 logx

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  10. Find derivative of each of the following functions: (logx)/x

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  11. Find derivative of each of the following functions: e^x/(1+x^2)

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  12. Find derivative of each of the following functions: (e^x sin x)/(sec...

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  13. Find derivative of each of the following functions: (e^x log x)/(x^2...

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  14. Find derivative of each of the following functions: (e^x(x-1))/(x+1)

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  15. Find derivative of each of the following functions: (e^x + sinx)/(1 ...

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  16. Find derivative of each of the following functions: xe^x sin x

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  17. Find derivative of each of the following functions: x^2 log x cos x

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  18. Find dy/dx when y = sin u, u = e^(sqrtt) and t = log x

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  19. Find the derivatives of the following functions at any point of their ...

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  20. Find the derivatives of the following functions at any point of their ...

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