Find the Derivative - d/dx y=4sin(x)cos(x)

Problem

d()/d(x)*4*sin(x)*cos(x)

Solution

1. Identify the expression as a product of two trigonometric functions multiplied by a constant.

2. Apply the double-angle identity for sine, which states sin(2*x)=2*sin(x)*cos(x) to simplify the expression before differentiating.

3. Rewrite the original expression using this identity.

y=2*(2*sin(x)*cos(x))

y=2*sin(2*x)

4. Apply the chain rule to find the derivative of 2*sin(2*x)

d(y)/d(x)=2*cos(2*x)⋅(d(2)*x)/d(x)

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

d(y)/d(x)=2*cos(2*x)⋅2

6. Simplify the resulting expression.

d(y)/d(x)=4*cos(2*x)

Final Answer

(d(4)*sin(x)*cos(x))/d(x)=4*cos(2*x)

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