Question

Differentiate tan²x w.r.t cos²x.

Answer 1

Let u = tan²x, v = cos²x 

Differentiate both w.r.t x 

\(\frac{du}{dx}\) = 2tan x. sec²x,

\(\frac{dv}{dx}\) = 2cosx(-sinx)

∴ \(\frac{du}{dv}\) = \(\frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2tanx.sec^2x}{2sinx.cosx}\)

= \(\frac{1}{sec^4x}\)