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

Problem

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

Solution

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

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

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

d(cos(2*x))/d(x)=−sin(2*x)⋅(d(2)*x)/d(x)

3. Differentiate the inner function 2*x with respect to x

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

4. Substitute the result back into the expression and multiply the constants.

3⋅(−sin(2*x)⋅2)=−6*sin(2*x)

Final Answer

(d(3)*cos(2*x))/d(x)=−6*sin(2*x)

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