Derivative of acos(x/2)
Answer
(-1/2)*sqrt((-1/4)*x^2+1)^(-1)
Derivative of acos(x/2)
- 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: (-1/2)*
The derivative of acos(x/2) is (-1/2)*sqrt((-1/4)*x^2+1)^(-1).
Instant step-by-step solution for acos(x/2)
Share this result
Derivative of acos(x/2) = (-1/2)*sqrt((-1/4)*x^2+1)^(-1) Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-acosx-minus-over-minus-2
How to find the derivative of acos(x/2)
To find the derivative of acos(x/2), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of x^4
Solve d/dx x^4
Derivative of 1/x
Solve d/dx 1/x
Derivative of 1/x^2
Solve d/dx 1/x^2
Derivative of x^(1/3)
Solve d/dx x^(1/3)
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of 1-x
Solve d/dx 1-x
Derivative of 10^x
Solve d/dx 10^x
Derivative of 2^x
Solve d/dx 2^x
Derivative of 2x
Solve d/dx 2x
Derivative of 3x^2
Solve d/dx 3x^2
Frequently Asked Questions
What is the derivative of acos(x/2)?▼
The derivative of acos(x/2) is (-1/2)*sqrt((-1/4)*x^2+1)^(-1).
How do you find the derivative of acos(x/2)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is (-1/2)*sqrt((-1/4)*x^2+1)^(-1).
Why is the derivative of acos(x/2) equal to (-1/2)*sqrt((-1/4)*x^2+1)^(-1)?▼
Because differentiation measures how a function changes — applying the rules to acos(x/2) yields (-1/2)*sqrt((-1/4)*x^2+1)^(-1). See the full step-by-step breakdown above.