Find the Derivative - d/dx 3sin(x)

Problem

(d(3)*sin(x))/d(x)

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

2. Apply the constant multiple rule by moving the coefficient 3 outside of the derivative.

(d(3)*sin(x))/d(x)=3d(sin(x))/d(x)

3. Recall the basic trigonometric derivative rule for the sine function, which is d(sin(x))/d(x)=cos(x)

4. Substitute the derivative of sin(x) back into the expression.

3d(sin(x))/d(x)=3*cos(x)

Final Answer

(d(3)*sin(x))/d(x)=3*cos(x)

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