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

Problem

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

Solution

1. Identify the constant and the function to be differentiated. The constant 2 can be moved outside the derivative.

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

2. Apply the power rule to the term cos(x) The power rule states that d(un)/d(x)=n*u(n−1)d(u)/d(x)

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

3. Differentiate the inner function cos(x) The derivative of cos(x) is −sin(x)

6*cos(x)*(−sin(x))

4. Simplify the expression by multiplying the terms together.

−6*cos(x)*sin(x)

Final Answer

(d(2)*cos(x))/d(x)=−6*cos(x)*sin(x)

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