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

Problem

(d(2)*cos(x))/d(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 the function.

(d(c)*ƒ(x))/d(x)=cd(ƒ(x))/d(x)

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

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

3. Differentiate the trigonometric function cos(x) using the standard derivative rule d(cos(x))/d(x)=−sin(x)

2d(cos(x))/d(x)=2*(−sin(x))

4. Simplify the expression by multiplying the constant and the derivative.

2*(−sin(x))=−2*sin(x)

Final Answer

(d(2)*cos(x))/d(x)=−2*sin(x)

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