Find the Derivative - d/dx 4cos(x)

Problem

(d(4)*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 that function.

2. Apply the constant multiple rule by moving the 4 outside of the derivative operator.

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

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

4. Substitute the derivative of cos(x) back into the expression.

4*(−sin(x))

5. Simplify the expression by multiplying the constant and the sine function.

−4*sin(x)

Final Answer

(d(4)*cos(x))/d(x)=−4*sin(x)

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