Derivative of sqrt(x^2+7)
Answer
(7+x^2)^(-1/2)*x
Derivative of sqrt(x^2+7)
- 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: (7+)^(-1/2)*x
The derivative of sqrt(x^2+7) is (7+x^2)^(-1/2)*x.
Instant step-by-step solution for sqrt(x^2+7)
Share this result
Derivative of sqrt(x^2+7) = (7+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-7
How to find the derivative of sqrt(x^2+7)
To find the derivative of sqrt(x^2+7), we use standard differentiation rules. Our AI-powered calculator breaks down the steps and explains the logic.
Practice More Problems
Derivative of ln(x)
Solve d/dx ln(x)
Derivative of -x
Solve d/dx -x
Derivative of x^(1/2)
Solve d/dx x^(1/2)
Derivative of sec(x)
Solve d/dx sec(x)
Derivative of sin(2x)
Solve d/dx sin(2x)
Derivative of sin(x)^2
Solve d/dx sin(x)^2
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)
Frequently Asked Questions
What is the derivative of sqrt(x^2+7)?▼
The derivative of sqrt(x^2+7) is (7+x^2)^(-1/2)*x.
How do you find the derivative of sqrt(x^2+7)?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is (7+x^2)^(-1/2)*x.
Why is the derivative of sqrt(x^2+7) equal to (7+x^2)^(-1/2)*x?▼
Because differentiation measures how a function changes — applying the rules to sqrt(x^2+7) yields (7+x^2)^(-1/2)*x. See the full step-by-step breakdown above.