Derivative of ln(cos(x))

Answer

-\frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)}

Derivative of ln(cos(x))

Rule Used: Chain Rule
Steps: Identify a composite function in $\log(\cos(x))$ : use the chain rule $\frac{d}{dx} f(g(x))$ = f'(g(x))·g'(x). The inner derivative is required because a stretch or shift of the input changes how fast the output moves.
Differentiate the outer function, then multiply by the inner derivative.
Final answer: - $\cos(x)^{-1}$ * $\sin(x)$

The derivative of ln(cos(x)) is -cos(x)^(-1)*sin(x).

Instant step-by-step solution for ln(cos(x))

Derivative LogarithmicIntermediate

Share this result

Share on X

Derivative of ln(cos(x)) = -cos(x)^(-1)*sin(x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-lncosx

How to find the derivative of ln(cos(x))

To find the derivative of ln(cos(x)), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.

Practice More Problems

Derivative of sec(x)

Solve d/dx sec(x)

Derivative of sin(2x)

Solve d/dx sin(2x)

Derivative of sin(x)^2

Solve d/dx sin(x)^2

Derivative of sin(x)

Solve d/dx sin(x)

Derivative of sinh(x)

Solve d/dx sinh(x)

Derivative of tan(x)^2

Solve d/dx tan(x)^2

Derivative of tan(x)

Solve d/dx tan(x)

Derivative of tanh(x)

Solve d/dx tanh(x)

Derivative of x*cos(x)

Solve d/dx x*cos(x)

Derivative of x*sin(x)

Solve d/dx x*sin(x)

Frequently Asked Questions

What is the derivative of ln(cos(x))?▼

The derivative of ln(cos(x)) is -cos(x)^(-1)*sin(x).

How do you find the derivative of ln(cos(x))?▼

Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is -cos(x)^(-1)*sin(x).

Why is the derivative of ln(cos(x)) equal to -cos(x)^(-1)*sin(x)?▼

Because differentiation measures how a function changes — applying the rules to ln(cos(x)) yields -cos(x)^(-1)*sin(x). See the full step-by-step breakdown above.

Support via PayPal

Support free development ❤️