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

Problem

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

Solution

1. Identify the trigonometric identity for the double angle of sine, which states that sin(2*x)=2*sin(x)*cos(x)

2. Substitute the identity into the expression to simplify the function before differentiating.

y=sin(2*x)

3. Apply the chain rule to find the derivative of sin(2*x) where the outer function is sin(u) and the inner function is u=2*x

d(y)/d(x)=cos(2*x)⋅(d(2)*x)/d(x)

4. Differentiate the inner function 2*x to get 2

d(y)/d(x)=cos(2*x)⋅2

5. Simplify the expression by moving the constant to the front.

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

Final Answer

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

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