Find the Derivative - d/dx 2cos(3x)

Problem

(d(2)*cos(3*x))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

(d(2)*cos(3*x))/d(x)=2d(cos(3*x))/d(x)

2. Apply the chain rule to the function cos(3*x) where the outer function is cos(u) and the inner function is u=3*x

d(cos(3*x))/d(x)=−sin(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. Combine the results by multiplying the constant, the derivative of the outer function, and the derivative of the inner function.

2⋅(−sin(3*x))⋅3=−6*sin(3*x)

Final Answer

(d(2)*cos(3*x))/d(x)=−6*sin(3*x)

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