If f(x) = _ x^2 ^ x^4 t ,dt, then f'(x) equals - Vidyadip

MCQ

If $f(x) = \int_{{x^2}}^{{x^4}} {\sin \sqrt t \,dt,} $ then $f'(x)$ equals

A
$\sin {x^2} - \sin x$
✓
$4{x^3}\sin {x^2} - 2x\sin x$
C
${x^4}\sin {x^2} - x\sin x$
D
None of these

✓

Answer

Correct option: B.

$4{x^3}\sin {x^2} - 2x\sin x$

b
(b) We have $f(x) = \int_{{x^2}}^{{x^4}} {\sin \sqrt t } \,dt$

$f'(x) = \frac{d}{{dx}}({x^4})(\sin \sqrt {{x^4}} ) - \frac{d}{{dx}}({x^2})\,(\sin \sqrt {{x^2}} )$

$ = 4{x^3}\sin {x^2} - 2x\sin x$.

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