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