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