Differentiate y = (4x - 2)^3 and evaluate dy/dx at x = 1.
Answer and explanation
Correct answer: D. 48
- Step 1: Apply the chain rule: dy/dx = 3 x 4 x (4x - 2)^2.
- Step 2: At x = 1 the inner expression equals 2.
- Step 3: dy/dx = 3 x 4 x 2^2 = 48.
Answer
48.
Why not the others: '12' omits the inner derivative 4 from the chain rule; '8' evaluates y instead of dy/dx; '96' does not lower the exponent by one.
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