Derivative of acos(x/3)
Answer
(-1/3)*sqrt((-1/9)*x^2+1)^(-1)
Derivative of acos(x/3)
- 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: (-1/3)*
The derivative of acos(x/3) is (-1/3)*sqrt((-1/9)*x^2+1)^(-1).
Instant step-by-step solution for acos(x/3)
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Derivative of acos(x/3) = (-1/3)*sqrt((-1/9)*x^2+1)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-acosx-minus-over-minus-3
How to find the derivative of acos(x/3)
To find the derivative of acos(x/3), 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 acos(x/3)?▼
The derivative of acos(x/3) is (-1/3)*sqrt((-1/9)*x^2+1)^(-1).
How do you find the derivative of acos(x/3)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is (-1/3)*sqrt((-1/9)*x^2+1)^(-1).
Why is the derivative of acos(x/3) equal to (-1/3)*sqrt((-1/9)*x^2+1)^(-1)?▼
Because differentiation measures how a function changes — applying the rules to acos(x/3) yields (-1/3)*sqrt((-1/9)*x^2+1)^(-1). See the full step-by-step breakdown above.