What is the derivative of g(x) = sin(4x)?
Answer and explanation
Correct answer: A. 4 cos(4x)
- Step 1: Apply the chain rule d/dx [sin(u)] = cos(u) * du/dx where u = 4x.
- Step 2: Since du/dx = 4, the derivative is 4 cos(4x).
Answer
4 cos(4x).
Why not the others: 'cos(4x)' neglects the inner derivative from the chain rule; '-4 cos(4x)' erroneously attaches a negative sign as if differentiating cosine; '-cos(4x)' combines both errors.
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