Derivative of (x^3+2)^5
Answer
15*(2+x^3)^4*x^2
Derivative of (x^3+2)^5
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in (+2)^5: 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: 15*(2+)^
The derivative of (x^3+2)^5 is 15*(2+x^3)^4*x^2.
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Derivative of (x^3+2)^5 = 15*(2+x^3)^4*x^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-x-minus-to-minus-the-minus-3-minus-plus-minus-2-minus-to-minus-the-minus-5
How to find the derivative of (x^3+2)^5
To find the derivative of (x^3+2)^5, 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^3+2)^5?▼
The derivative of (x^3+2)^5 is 15*(2+x^3)^4*x^2.
How do you find the derivative of (x^3+2)^5?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 15*(2+x^3)^4*x^2.
Why is the derivative of (x^3+2)^5 equal to 15*(2+x^3)^4*x^2?▼
Because differentiation measures how a function changes — applying the rules to (x^3+2)^5 yields 15*(2+x^3)^4*x^2. See the full step-by-step breakdown above.