Find the Derivative - d/d@VAR (f-g)(-3)

Problem

d()/d(x)*(ƒ−g)*(−3)

Solution

1. Identify the expression as the derivative of a difference of two functions evaluated at a specific point, x=−3

2. Apply the sum/difference rule for derivatives, which states that the derivative of a difference is the difference of the derivatives.

d()/d(x)*(ƒ(x)−g(x))=ƒ(x)′−g(x)′

3. Recognize that the derivative of a function evaluated at a constant point is the derivative of a constant value.

4. Apply the constant rule for differentiation, which states that the derivative of any constant value is zero.

d()/d(x)*(C)=0

5. Conclude that since (ƒ−g)*(−3) is a specific numerical value (a constant), its derivative with respect to x is zero.

Final Answer

d()/d(x)*(ƒ−g)*(−3)=0

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