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According to Leibritz differentiation un...

According to Leibritz differentiation under the sign of integration can be performed as as below.
(i) `(d)/(dx)[int_(phi(x))^(Psi(x))f(t)dt]=f{Psi(x)}xx(d)/(dx){Psi(x)}-f{phi(x)}xx(d)/(dx){phi(x)}`
(ii) `(d)/(dx)[int_(phi(x))^(Psi(x))f(x,t)dt]=int_(phi(x))^(Psi(x))(del)/(delx)(f(x,t)dt)+f(x,Psi(x))xx(d)/(dx)Psi(x)-f(x,phi(x))xx(d)/(dx)(phi(x))`
`int_(x^(2))^(x^(3))cost^(2)dt` has the derivative

A

`3x^(2)cosx^(3)-2xcosx^(2)`

B

`3x^(2)cosx^(6)-2xcosx^(4)`

C

`cosx^(6)-cosx^(4)`

D

none of these

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