Derivative of (4x-4)^3
Answer
12*(-4+4*x)^2
Derivative of (4x-4)^3
- Rule Used
- Chain Rule
- Steps
- Identify a composite function in (-4)^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: 12*(-4+)^2
The derivative of (4*x-4)^3 is 12*(-4+4*x)^2.
Instant step-by-step solution for (4x-4)^3
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Derivative of (4x-4)^3 = 12*(-4+4*x)^2 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-4x-minus-4-minus-to-minus-the-minus-3
How to find the derivative of (4x-4)^3
To find the derivative of (4x-4)^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 (4x-4)^3?▼
The derivative of (4x-4)^3 is 12*(-4+4*x)^2.
How do you find the derivative of (4x-4)^3?▼
Apply the standard differentiation rules — the key rule used here is the Chain Rule. The step-by-step result is 12*(-4+4*x)^2.
Why is the derivative of (4x-4)^3 equal to 12*(-4+4*x)^2?▼
Because differentiation measures how a function changes — applying the rules to (4x-4)^3 yields 12*(-4+4*x)^2. See the full step-by-step breakdown above.