How do you differentiate $f (x) = \frac{{sin}^{2} x}{{cos}^{2} x}$ $f(x)=sin^2x/cos^2x$ ?

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Answer 1 · 2016-12-14T14:13:07

$f'(x) = 2sec^2xtanx$

We know that $sintheta/costheta = tantheta$ . So $f(x) = sin^2x/cos^2x = tan^2x = (tanx)(tanx)$ .

We know the derivative of $tanx$ is $sec^2x$ . By the product rule;

$f'(x) = sec^2xtanx + sec^2xtanx$

$f'(x) = 2sec^2xtanx$

Hopefully this helps!

How do you differentiate f(x)=sin^2x/cos^2xf(x)=sin2xcos2xf(x)=sin^2x/cos^2x?