Find the derivative of `f(tanx)wdotrdottg(secx)a tx=pi/4,` where `f^(prime)(1)=2a n dg^(prime)(sqrt(2))=4.`

Find the derivative of f(tanx) w.r.t. g(secx) at x=pi/4 , where f^(prime)(1)=2 and g^(prime)(sqrt(2))=4 .

The derivative of f(tan x)w*r.t.g(sec x) at x=(pi)/(4), where f'(1)=2 and g'(sqrt(2))=4

If f'(1)=-2sqrt(2) and g'(sqrt(2))=4, then the derivative of f(tan x) with respect to g(sec x) at x=(pi)/(4), is 1(b)-1(c)2(d)4

Find the derivative of the following functions : 2tanx-7secx

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a)(-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c)(-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

Statement 1: If both functions f(t)a n dg(t) are continuous on the closed interval [1,b], differentiable on the open interval (a,b) and g^(prime)(t) is not zero on that open interval, then there exists some c in (a , b) such that (f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a)) Statement 2: If f(t)a n dg(t) are continuou and differentiable in [a, b], then there exists some c in (a,b) such that f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a) from Lagranes mean value theorem.

What is the derivative of the function f(x)=e^(tanx)+ln(secx)-e^(lnx)" at "x=(pi)/(4)?