Differentiate y = tan(3x) with respect to x.
Answer and explanation
Correct answer: D. 3 sec^2(3x)
- Step 1: Apply the derivative rule d/dx [tan(u)] = sec^2(u) * du/dx.
- Step 2: Here u = 3x, so du/dx = 3. Thus dy/dx = 3 sec^2(3x).
Answer
3 sec^2(3x).
Why not the others: 'sec^2(3x)' forgets to multiply by the inner derivative 3; '-3 sec^2(3x)' erroneously introduces a negative sign; '3 tan(3x) sec(3x)' is the derivative of sec(3x).
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