Final answer to the problem
$-\tan\left(x\right)$
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Step-by-step Solution
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1
Apply the formula: $\frac{d}{dx}\left(\ln\left(x\right)\right)$$=\frac{1}{x}\frac{d}{dx}\left(x\right)$
$\frac{1}{\cos\left(x\right)}\frac{d}{dx}\left(\cos\left(x\right)\right)$
Learn how to solve calcul différentiel problems step by step online.
$\frac{1}{\cos\left(x\right)}\frac{d}{dx}\left(\cos\left(x\right)\right)$
Learn how to solve calcul différentiel problems step by step online. d/dx(ln(cos(x))). Apply the formula: \frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right). Apply the trigonometric identity: \frac{d}{dx}\left(\cos\left(\theta \right)\right)=-\sin\left(\theta \right). Apply the formula: a\frac{b}{x}=\frac{ab}{x}. Apply the formula: 1x=x, where x=-\sin\left(x\right).
Final answer to the problem
$-\tan\left(x\right)$
