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

Problem

d()/d(x)*(sin(2*x)−2*sin(x))

Solution

1. Apply the sum rule for differentiation to separate the terms.

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

2. Apply the chain rule to the first term, where the outer function is sin(u) and the inner function is u=2*x

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

3. Differentiate the inner function of the first term.

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

4. Apply the constant multiple rule to the second term.

(d(2)*sin(x))/d(x)=2⋅d(sin(x))/d(x)

5. Differentiate the sine function in the second term.

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

6. Combine the results to find the final derivative.

2*cos(2*x)−2*cos(x)

Final Answer

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

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