Difference Rule
Definition
The Difference Rule states that the derivative of a difference of two functions is the difference of their derivatives. Mathematically, if $f(x)$ and $g(x)$ are differentiable, then $(f-g)' = f' - g'$.
5 Must Know Facts For Your Next Test
- The Difference Rule applies to any pair of differentiable functions.
- It simplifies the process of finding derivatives when dealing with subtraction.
- The rule can be used in conjunction with other differentiation rules like the Product and Quotient Rules.
- You can apply this rule as $(f-g)'(x) = f'(x) - g'(x)$ for all $x$ in the domain where both functions are differentiable.
- This rule is often introduced alongside the Sum Rule, which deals with addition instead of subtraction.
Review Questions
- What is the derivative of $h(x) = f(x) - g(x)$ using the Difference Rule?
- If $f(x) = x^2$ and $g(x) = \sin(x)$, what is $(f-g)'(x)?$
- How does the Difference Rule simplify finding the derivative of a function defined by subtraction?
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Related terms
Sum Rule: The Sum Rule states that the derivative of a sum of two functions is the sum of their derivatives: $(f+g)' = f' + g'.$
Product Rule: The Product Rule states that the derivative of a product of two functions is given by $(fg)' = f'g + fg'.$
Quotient Rule: The Quotient Rule states that the derivative of a quotient is given by $\left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^2}$, provided that $g \neq 0$.
