Question

What is the differential coefficient of sec^2x with respect to tanx ?​

Answer 1

Step-by-step explanation:

$let \: \: \sec^{2} (x) = u \: \: and \: \: \tan(x) = v$

Diffrnentiating both functions w.r.t x

$\frac{du}{dx} = 2 \sec(x). \sec(x) \tan(x) \: \: and \: \: \frac{dv}{dx} = \sec^{2} (x )$

Now,

$\frac{du}{dv} = \frac{ \frac{du}{dx} }{ \frac{dv}{dx} } = \frac{2 \sec^{2} (x) \tan(x) }{ \sec^{2} (x) }$

$= 2 \tan(x)$