Question

f(x)=0ʃ g(x) 1/(1+t)3/2, g(x)=0ʃcos(x) 1+(sin(t2)),find df/dx(π/2)

Answer 1

Mmm I don't quite understand what you've written.
Is this what it looks like?

\[\Large\bf\sf f(x)\quad=\quad \oint g(x)\cdot \frac{1}{(1+t)^{3/2}}\;dt\]
\[\Large\bf\sf g(x)\quad=\quad \oint \cos x(1+\sin t^2)\;dt\]

Is the differential supposed to be t, or x .. or what's going on?
Maybe you can clarify .

Answer 2

probably t

Answer 3

as I thought first we do the integration on g(x) then on f(x) then replace the value