Derivative of sqrt(x^2+8)
Answer
(8+x^2)^(-1/2)*x
Derivative of sqrt(x^2+8)
- 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: (8+)^(-1/2)*x
The derivative of sqrt(x^2+8) is (8+x^2)^(-1/2)*x.
Instant step-by-step solution for sqrt(x^2+8)
Share this result
Derivative of sqrt(x^2+8) = (8+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-8
How to find the derivative of sqrt(x^2+8)
To find the derivative of sqrt(x^2+8), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of sin(x)
Solve d/dx sin(x)
Derivative of sinh(x)
Solve d/dx sinh(x)
Derivative of sqrt(x)
Solve d/dx sqrt(x)
Derivative of tan(x)^2
Solve d/dx tan(x)^2
Derivative of tan(x)
Solve d/dx tan(x)
Derivative of tanh(x)
Solve d/dx tanh(x)
Derivative of x*cos(x)
Solve d/dx x*cos(x)
Derivative of x*e^x
Solve d/dx x*e^x
Derivative of x*ln(x)
Solve d/dx x*ln(x)
Derivative of x+1
Solve d/dx x+1
Frequently Asked Questions
What is the derivative of sqrt(x^2+8)?▼
The derivative of sqrt(x^2+8) is (8+x^2)^(-1/2)*x.
How do you find the derivative of sqrt(x^2+8)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is (8+x^2)^(-1/2)*x.
Why is the derivative of sqrt(x^2+8) equal to (8+x^2)^(-1/2)*x?▼
Because differentiation measures how a function changes — applying the rules to sqrt(x^2+8) yields (8+x^2)^(-1/2)*x. See the full step-by-step breakdown above.