Derivative of e^(cos(x))
Answer
-119696244^(-cos(x))*325368125^cos(x)*sin(x)
Derivative of e^(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: -119696244^(-)*325368125^*
The derivative of e^(cos(x)) is -119696244^(-cos(x))*325368125^cos(x)*sin(x).
Instant step-by-step solution for e^(cos(x))
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Derivative of e^(cos(x)) = -119696244^(-cos(x))*325368125^cos(x)*sin(x) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-e-minus-to-minus-the-minus-cosx
How to find the derivative of e^(cos(x))
To find the derivative of e^(cos(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 e^(cos(x))?▼
The derivative of e^(cos(x)) is -119696244^(-cos(x))*325368125^cos(x)*sin(x).
How do you find the derivative of e^(cos(x))?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is -119696244^(-cos(x))*325368125^cos(x)*sin(x).
Why is the derivative of e^(cos(x)) equal to -119696244^(-cos(x))*325368125^cos(x)*sin(x)?▼
Because differentiation measures how a function changes — applying the rules to e^(cos(x)) yields -119696244^(-cos(x))*325368125^cos(x)*sin(x). See the full step-by-step breakdown above.