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

Problem

d()/d(x)−2*cos(x)*sin(x)

Solution

1. Identify the expression as a product of two functions, which can be simplified using the double-angle identity for sine: sin(2*x)=2*sin(x)*cos(x)

2. Rewrite the original expression using this identity to make the differentiation easier.

−2*cos(x)*sin(x)=−sin(2*x)

3. Apply the chain rule to differentiate −sin(2*x) The derivative of sin(u) is cos(u) and the derivative of the inner function 2*x is 2

(d(−)*sin(2*x))/d(x)=−cos(2*x)⋅2

4. Simplify the resulting expression by moving the constant to the front.

−2*cos(2*x)

Final Answer

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

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