Step-by-step Solution

Find the derivative of $\ln\left(\cos\left(3x\right)\right)$

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Step-by-step solution

Problem to solve:

$\frac{d}{dx}\left(\ln\left(\cos\left(3x\right)\right)\right)$

Solving method

Learn how to solve differential calculus problems step by step online.

$\frac{1}{\cos\left(3x\right)}\frac{d}{dx}\left(\cos\left(3x\right)\right)$

Unlock this full step-by-step solution!

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(cos(3*x)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of the linear function times a constant, is equal to the constant.

Final Answer

$\frac{-3\sin\left(3x\right)}{\cos\left(3x\right)}$
$\frac{d}{dx}\left(\ln\left(\cos\left(3x\right)\right)\right)$

Main topic:

Differential Calculus

Related Formulas:

4. See formulas

Time to solve it:

~ 0.03 s