Derivada de ln(cos(x))
Answer
-cos(x)^(-1)*sin(x)
Derivative of ln(cos(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: -*
A derivada de ln(cos(x)) é -cos(x)^(-1)*sin(x).
Solução passo a passo instantânea para ln(cos(x))
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Derivative of ln(cos(x)) = -cos(x)^(-1)*sin(x) Solve step-by-step for free: https://derivativecalculatorai.com/pt/derivative-of-lncosx
Como encontrar a derivada de ln(cos(x))
Para encontrar a derivada de ln(cos(x)), usamos regras de diferenciação padrão. Nossa calculadora com IA detalha os passos e explica a lógica.
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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.