`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 ("lim")_(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, then find the value of f^(prime)(0)dot a) 4 (b) 2 (c) 0 (d) 1

If f(x)=1+1/x int_1^x f(t) dt, then the value of (e^-1) is

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))

Iff(x)=int_((x^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta))dtheta, then find the value of f^(prime)(pi/2)dot

If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then find the value of (lim)_(xvec0)(((dy)/(dz)))/x

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If ("lim")_(xveca)[f(x)+g(x)]=2a n d ("lim")_(xveca)[f(x)-g(x)]=1, then find the value of ("lim")_(xveca)f(x)g(x)dot

Evaluate: int_(-1)^4f(x)dx=4a n dint_2^4(3-f(x))dx=7, then find the value of int_2^(-1)f(x)dxdot

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)(x), then the reciprocal of g^(prime)((-7)/6) is_________