If-f-x-a-a-x-3-dt-1-sin-2-t-dt-1-sin-2-t-then-f-x-

Question Number 122434 by benjo_mathlover last updated on 17/Nov/20

I f f (x) = \int_{a}^{(\underset{a}{\int^{x^{3}}} \frac{d t}{1 + \sin^{2} t})} (\frac{d t}{1 + \sin^{2} t})

t h e n f^{'} (x) ?

Answered by liberty last updated on 17/Nov/20

f^{'} (x) = \frac{{(x^{3})}^{'}}{(1 + \sin^{2} (x^{3})) . (1 + \sin^{2} (\underset{1}{\int^{x^{3}}} \frac{dt}{1 + \sin^{2} t}))}

f^{'} (x) = \frac{{3 x}^{2}}{(1 + 2 \sin^{2} (x^{3})) . (1 + \sin^{2} (\underset{1}{\int^{x^{3}}} \frac{dt}{1 + \sin^{2} t}))}

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