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

Problem

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

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

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

2. Apply the chain rule to the function sin(2*x) 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 2*x with respect to x

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

4. Substitute the derivative of the inner function back into the expression.

2⋅cos(2*x)⋅2

5. Simplify the expression by multiplying the constants.

4*cos(2*x)

Final Answer

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

Want more problems? Check here!