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

Problem

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

Solution

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

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

2. Apply the chain rule for the function cos(u) where u=2*x

d(cos(u))/d(x)=−sin(u)d(u)/d(x)

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

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

4. Combine the results by multiplying the outer derivative by the inner derivative.

2*(−sin(2*x)⋅2)

5. Simplify the expression by multiplying the constants.

−4*sin(2*x)

Final Answer

(d(2)*cos(2*x))/d(x)=−4*sin(2*x)

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