Question

Calcule o valor da derivada da função f(x) = sen(x)/cos(x)

Answer 1

Olá!

$\\ \mathsf{f(x) = \frac{\sin x}{\cos x}} \\\\ \mathsf{f'(x) = \frac{(\sin x)' \cdot \cos x - \sin x \cdot (\cos x)'}{(\cos^2 x)}} \\\\ \mathsf{f'(x) = \frac{\cos x \cdot \cos x - \sin x \cdot (- \sin x)}{\cos^2 x}} \\\\ \mathsf{f'(x) = \frac{\cos^2 x + \sin^2 x}{\cos^2 x}} \\\\ \mathsf{f'(x) = \frac{1}{\cos^2 x}} \\\\ \boxed{\mathsf{f'(x) = \sec^2 x}}$