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

Problem

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

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of that function.

2. Apply the constant multiple rule by moving the coefficient 2 outside of the derivative operation.

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

3. Recall the basic trigonometric derivative rule for the sine function, which is d(sin(x))/d(x)=cos(x)

4. Substitute the derivative of sin(x) back into the expression to find the final result.

2⋅cos(x)=2*cos(x)

Final Answer

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

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