Question

Find the derivative of f(tanx) w.r.t. f(secx) at x=pi/4 , when f(1) = 2 , g(root2) = 4

Answer 1

Hi ..here is your solution..
hope u understand

Answer 2

Answer:

Step-by-step explanation:

Differentiate f(tanx) with respect to x, we get

$\frac{df(tanx)}{dx}=sec^{2}x$                            (1)

Now, Differentiate f(secx) with respect to x, we get

$\frac{df(secx)}{dx}=secxtanx$                          (2)

Divide (1) by (2), we get

$\frac{df(tanx)}{df(secx)}=\frac{sec^{2}x}{secxtanx}$

=$\frac{secx}{tanx}$

=$\frac{1}{sinx}$

Now, value of $\frac{df(tanx)}{df(secx)}$ at $x=\frac{{\pi}}{4}$ is:

$\frac{df(tanx)}{df(secx)}=\frac{1}{sin\frac{{\pi}}{4}}=\sqrt{2}$.