Find the Derivative - d/dx 3cos(x)

Problem

(d(3)*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.

2. Apply the constant multiple rule by moving the constant 3 outside of the derivative.

(d(3)*cos(x))/d(x)=3d(cos(x))/d(x)

3. Apply the trigonometric derivative rule for the cosine function, which is d(cos(x))/d(x)=−sin(x)

3d(cos(x))/d(x)=3*(−sin(x))

4. Simplify the expression by multiplying the terms.

3*(−sin(x))=−3*sin(x)

Final Answer

(d(3)*cos(x))/d(x)=−3*sin(x)

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