Differentiate y = (4x + 1)^2 and evaluate dy/dx at x = 1.
Answer and explanation
Correct answer: B. 40
- Step 1: Apply the chain rule: dy/dx = 2 x 4 x (4x + 1)^1.
- Step 2: At x = 1 the inner expression equals 5.
- Step 3: dy/dx = 2 x 4 x 5^1 = 40.
Answer
40.
Why not the others: '10' omits the inner derivative 4 from the chain rule; '25' evaluates y instead of dy/dx; '200' does not lower the exponent by one.
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