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

Problem

d(cos(x))/d(x)

Solution

1. Identify the outer and inner functions to apply the Chain Rule, where the outer function is u2 and the inner function is u=cos(x)

2. Apply the Power Rule to the outer function, which gives 2*cos(x)

3. Apply the Chain Rule by multiplying by the derivative of the inner function, d(cos(x))/d(x)

4. Differentiate the inner function to get −sin(x)

5. Multiply the components together to get 2*cos(x)⋅(−sin(x))

6. Simplify the expression using the trigonometric identity sin(2*x)=2*sin(x)*cos(x)

Final Answer

d(cos(x))/d(x)=−2*sin(x)*cos(x)

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