If f(3)=7, f^'(3)=2, g(3)=6, and g^'(3)=-10, find (a) (f-g)^'(3) (b) (f ·g)^'(3) (c) (g / f)^'(3

step 1 So here we're asked to apply derivative rules. The difference rule will help us in the first, wh

If f(3)=7, f^'(3)=2, g(3)=6, and g^'(3)=-10, find (a)...

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Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that involves finding the rate at which a function changes at any point. It forms the basis for determining slopes of tangent lines, instantaneous rates of change, and for understanding the behavior of functions.

Sum and Difference Rule

The sum and difference rule states that the derivative of the sum (or difference) of two functions is equal to the sum (or difference) of their derivatives. This rule simplifies the process of differentiation by allowing one to differentiate each term separately.

Product Rule

The product rule is used to differentiate functions that are multiplied together. It states that the derivative of the product of two functions is given by the derivative of the first function multiplied by the second function, plus the first function multiplied by the derivative of the second function.

Quotient Rule

The quotient rule is applied when differentiating a function that is the ratio of two differentiable functions. It asserts that the derivative of a quotient is found by taking the derivative of the numerator multiplied by the denominator minus the numerator multiplied by the derivative of the denominator, and dividing the result by the square of the denominator.

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