Derivative of (x^2-2)^4
Answer
8*(-2+x^2)^3*x
Derivative of (x^2-2)^4
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in (-2)^4: 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*(-2+)^
The derivative of (x^2-2)^4 is 8*(-2+x^2)^3*x.
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Derivative of (x^2-2)^4 = 8*(-2+x^2)^3*x Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-2-minus-2-minus-to-minus-the-minus-4
How to find the derivative of (x^2-2)^4
To find the derivative of (x^2-2)^4, 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 (x^2-2)^4?▼
The derivative of (x^2-2)^4 is 8*(-2+x^2)^3*x.
How do you find the derivative of (x^2-2)^4?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 8*(-2+x^2)^3*x.
Why is the derivative of (x^2-2)^4 equal to 8*(-2+x^2)^3*x?▼
Because differentiation measures how a function changes — applying the rules to (x^2-2)^4 yields 8*(-2+x^2)^3*x. See the full step-by-step breakdown above.