`Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4),` then find the value of `f^(prime)(2)`

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

If f(x)=5^(g(x)) and g(x)=int_(2)^(x^(2))(t)/(ln(1+t^(2))dt) ,then find the value of f'(sqrt(2))

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(tdt)/(1+t^(4)) then f'(2) has the value equal to: a.2/17 b.0 c.1 d.(2)/(5)

Q.if the function f(x)=x^(3)+(e^(x))/(2) and g(x)=f^(-1)(x), then find the value of g'(1)

f(x)=int_(1)^(x)(tan^(-1)(t))/(t)dt,x in R^(+), then find the value of f(e^(2))-f((1)/(e^(2)))

int_(0)^(ln3)(e^(x)+x)f(x)+(e^(x)+1)int_(0)^(x)f(t)dt=p(q+ln3)t then find the value of (p+q)

If lim_(t rarr x)(e^(t)f(x)-e^(x)f(t))/((t-x)(f(x))^(2))=2 and f(0)=(1)/(2), then find the value of f'(0)*4(b)2(c)0(d)1

Let f(x)=e^(x)+2x+1 then find the value of int_(2)^(e+3)f^(-1)(x)dx

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).

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx