`f(x)=int_(loge x)^x(dt)/(x+t),t h e n f i n df^(prime)(x)`

If f(x)=int_(log_(e)x)^(x)(dt)/(x+t) then f'(x)=

let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) t h e n f i n d (h^(prime)(x))/(h(x))

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to a) -cosx (b) -sinx c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

If f(x)=cosx-int_0^x(x-t)f(t)dt ,t h e nf^(primeprime)(x)+f(x) is equal to (a) -cosx (b) -sinx (c) int_0^x(x-t)f(t)dt (d) 0

Let f(x)=int_(0)^(x)(sint)/(t)dt(x gt 0) then f(x) has (n in N)

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

L e tf:[1,oo)->Ra n df(x)=int_1^x(e^t)/t dt-e^xdotT h e n f(x) is an increasing function lim_(x->oo)f(x)->oo f^(prime)(x) has a maxima at x=e f(x) is a decreasing function

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .