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

Problem

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

Solution

1. Identify the constant multiple rule, which allows the constant 3 to be moved outside the derivative.

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

2. Apply the chain rule, which states that the derivative of sin(u) is cos(u)⋅d(u)/d(x) where u=3*x

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

3. Differentiate the inner function 3*x with respect to x

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

4. Substitute the derivative of the inner function back into the expression.

3⋅cos(3*x)⋅3

5. Simplify the expression by multiplying the constants.

9*cos(3*x)

Final Answer

(d(3)*sin(3*x))/d(x)=9*cos(3*x)

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