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

Problem

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

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=2*x

2. Apply the Chain Rule by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

d(sin(u))/d(u)⋅d(u)/d(x)

3. Differentiate the outer function sin(u) which results in cos(u)

cos(2*x)⋅(d(2)*x)/d(x)

4. Differentiate the inner function 2*x with respect to x which results in 2

cos(2*x)⋅2

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

2*cos(2*x)

Final Answer

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

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