If `d/(dx)[int_0^(g(x)) f(t) dt]= 2xsin(2x^2)e^(asin^2(x^2))cos(bsinx^2)` then

(d)/(dx)(int_(f(x))^(g(x)) phi(t)dt) is equal to

(d)/(dx)(int_(f(x))^(g(x))phi(t)dt) is equal to

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

If (d)/(dx)(int_(0)^(y)e^(-t^(2))dt+int_(0)^(x^(2)) sin^(2) tdt)=0, "find" (dy)/(dx).

(d)/(dx) int_(2)^(x^(2)) (t -1) dt is equal to

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

int_0^2 e^x d x

(d)/(dx)int_(t^(2))^(x^(3))(dt)/(sqrt(x^(2)+t^(4)))