lf `f(x) = 5^(g(x)) and g(x)=int_2^(x^2)t/(ln(1+t^2) dt`, then find the value of `f'(sqrt2)`.

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(tdt)/(1+t^(4)), then find the value of f'(2)

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(dt)/(1+t^(4)) then f'(2) is equal to

Given a funtion g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f ''(1)+f''(1).

Given a function g, continous everywhere such that g (1)=5 and int _(0)^(1) g (t) dt =2. If f (x) =1/2 int _(0) ^(x) (x -t)^(2) g (t) dt, then find the value of f '(1)+f''(1).

Let f,g:(0,oo)rarr R be two functions defined by f(x)=int_(-x)^(x)(|t|-t^(2))e^(-t^(2))dt and g(x)=int_(0)^(x^(2))t^(1/2)e^(-t)dt .Then,the value of 9(f(sqrt(log_(e)9))+g(sqrt(log_(e)9))) is equal to

Suppose f and g are two functions such that f,g: R -> R f(x)=ln(1+sqrt(1+x^2)) and g(x)=ln(x+sqrt(1+x^2)) then find the value of xe^(g(x))f(1/x)+g'(x) at x=1

If int_(0)^(x) f(t)dt=x+int_(x)^(1)t f(t)dt , find the value of f(1).

If f(x) = 1/x^(2) int_2^(x)[t^(2)+f^(')(t)]dt, then f^(')(2) =

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then minimum value of f (x) is: