Question

Find f'(x) [ diffretiation].



$f(x)=\int_{x}^{x^2}x\:sint\:dt$


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Answer 1

Your question has a little spelling mistake.

It should be >>

Find f'(x) [ differentiation].

$f(x)=\int_{x}^{x^2}x\:sint\:dt$

ANSWER

$f'(x)\implies -Cosx^{2} + Cosx + 2x^{2} Sinx^{2} - x\:Sinx$

Step By Step Explanation

We have ,

f(x)=$\int_{x}^{x^{2} } x\:sin\:t\:dt$

$\implies f(x)= x\int_{x}^{x^{2} }\: Sin\:t\:dt$

$\implies f'(x)=1.\int_{x}^{x^{2} }\: Sin\:t\:dt + x.(2x .Sinx^{2} - 1.Sinx)$

$\implies f'(x)=[-Cosx]_{x}^{x^{2} } + 2x^{2}Sinx^{2} - x Sinx$

$\implies f'(x)= -Cosx^{2} + Cosx + 2x^{2} Sinx^{2} - x\:Sinx$

Answer 2

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