Derivative of ln(sin(x))
Answer
cos(x)*sin(x)^(-1)
Derivative of ln(sin(x))
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in : use the chain rule = 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: *
The derivative of ln(sin(x)) is cos(x)*sin(x)^(-1).
Instant step-by-step solution for ln(sin(x))
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Derivative of ln(sin(x)) = cos(x)*sin(x)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-lnsinx
How to find the derivative of ln(sin(x))
To find the derivative of ln(sin(x)), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
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Frequently Asked Questions
What is the derivative of ln(sin(x))?▼
The derivative of ln(sin(x)) is cos(x)*sin(x)^(-1).
How do you find the derivative of ln(sin(x))?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is cos(x)*sin(x)^(-1).
Why is the derivative of ln(sin(x)) equal to cos(x)*sin(x)^(-1)?▼
Because differentiation measures how a function changes — applying the rules to ln(sin(x)) yields cos(x)*sin(x)^(-1). See the full step-by-step breakdown above.