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

Problem

d()/d(x)*2*cos2(x)

Solution

1. Identify the structure of the expression as a constant multiplied by a function raised to a power, which requires the power rule and the chain rule.

2. Apply the constant multiple rule by pulling the constant 2 out of the derivative.

2d(cos2(x))/d(x)

3. Apply the power rule to the term cos2(x) which brings the exponent down and reduces it by one.

2⋅2*cos(x)⋅d(cos(x))/d(x)

4. Apply the chain rule by multiplying by the derivative of the inner function, cos(x)

4*cos(x)⋅(−sin(x))

5. Simplify the expression by combining the terms.

−4*sin(x)*cos(x)

6. Apply the double angle identity sin(2*x)=2*sin(x)*cos(x) to further simplify the result.

−2*(2*sin(x)*cos(x))=−2*sin(2*x)

Final Answer

(d(2)*cos2(x))/d(x)=−2*sin(2*x)

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