Derivative of (x^2+3)^5
Answer
10*(3+x^2)^4*x
Derivative of (x^2+3)^5
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in (+3)^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: 10*(3+)^
The derivative of (x^2+3)^5 is 10*(3+x^2)^4*x.
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How to find the derivative of (x^2+3)^5
To find the derivative of (x^2+3)^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^2+3)^5?▼
The derivative of (x^2+3)^5 is 10*(3+x^2)^4*x.
How do you find the derivative of (x^2+3)^5?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 10*(3+x^2)^4*x.
Why is the derivative of (x^2+3)^5 equal to 10*(3+x^2)^4*x?▼
Because differentiation measures how a function changes — applying the rules to (x^2+3)^5 yields 10*(3+x^2)^4*x. See the full step-by-step breakdown above.