If y = sin(3x), dy/dx = ?

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Multiple Choice

If y = sin(3x), dy/dx = ?

Explanation:
Using the chain rule: when differentiating sin(u) with respect to x, you get cos(u) · du/dx. Here u = 3x, so du/dx = 3. Multiply: dy/dx = 3 cos(3x). The other forms would come from differentiating related functions (for example, the derivative of cos(3x) is -3 sin(3x), and differentiating sin(3x) without the inner-derivative factor would give cos(3x) instead of 3 cos(3x)). So the correct derivative is 3 cos(3x).

Using the chain rule: when differentiating sin(u) with respect to x, you get cos(u) · du/dx. Here u = 3x, so du/dx = 3. Multiply: dy/dx = 3 cos(3x). The other forms would come from differentiating related functions (for example, the derivative of cos(3x) is -3 sin(3x), and differentiating sin(3x) without the inner-derivative factor would give cos(3x) instead of 3 cos(3x)). So the correct derivative is 3 cos(3x).

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