Differentiate tan2x w.r.t cos2x.

1.	Differentiate tan2x w.r.t cos2x.
Answer» Let u = tan²x, v = cos²x Differentiate both w.r.t x \(\frac{du}{dx}\) = 2tan x. sec²x, \(\frac{dv}{dx}\) = 2cosx(-sinx) ∴ \(\frac{du}{dv}\) = \(\frac{\frac{du}{dx}}{\frac{dv}{dx}} = \frac{2tanx.sec^2x}{2sinx.cosx}\) = \(\frac{1}{sec^4x}\)

Answer»

Let u = tan²x, v = cos²x

Differentiate both w.r.t x

\(\frac{du}{dx}\) = 2tan x. sec²x,

\(\frac{dv}{dx}\) = 2cosx(-sinx)

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

= \(\frac{1}{sec^4x}\)

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