The derivative of f(tanx) w.r.t. g(sec x) at x=(π/4), where f '(1)=2 and g'(√2)=4 is

Question

The derivative of f(tanx) w.r.t. g(sec x) at x=(π/4), where f '(1)=2 and g'(√2)=4 is (A) (1/√2) (B) √2 (C) 1 (D) 0

Tardigrade Admin · Accepted Answer

Now, (df(tan x)/dg(sec x)) =(f '(tan x)sec2 x/g'(sec x)sec x tan x) =(f '(tan x)sec x/g'(sec x)tan x) (df (tan x)/dg(sec x))|at x=π/4 =(f '(1)√2/g'(√2)⋅1) =(2√2/4⋅1)=(1/√2)

Q. The derivative of $f (t an x)$ w.r.t. $g (sec x)$ at $x = \frac{π}{4}$ , where $f^{'} (1) = 2$ and $g^{'} (2) = 4$ is

$\frac{1}{2}$

$2$

$1$

$0$

Q. The derivative of f(tanx) w.r.t. g(secx) at x=4π​, where f′(1)=2 and g′(2​)=4 is

2​1​

2​

1

0

Now, dg(secx)df(tanx)​ =g′(secx)secxtanxf′(tanx)sec2x​ =g′(secx)tanxf′(tanx)secx​ dg(secx)df(tanx)​∣∣​atx=π/4​ =g′(2​)⋅1f′(1)2​​ =4⋅122​​=2​1​

Q. The derivative of $f (t an x)$ w.r.t. $g (sec x)$ at $x = \frac{π}{4}$ , where $f^{'} (1) = 2$ and $g^{'} (2) = 4$ is

$\frac{1}{2}$

$2$

$1$

$0$