AP Calculus BC / Unit 2: Differentiation: Definition and Fundamental Properties
2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
Notes
- Constant: $\displaystyle \frac{d}{dx}c=0$.
- Constant multiple: $\displaystyle \frac{d}{dx}[cf(x)]=cf'(x)$.
- Sum and difference: differentiate term by term.
Practice
$\displaystyle \frac{d}{dx}(4x^3-5x+9)=$
Term by term; the constant 9 has derivative 0.
If $f'(2)=3$ and $g'(2)=-1$, find $\displaystyle \frac{d}{dx}[2f(x)-5g(x)]$ at $x=2$.
$2(3)-5(-1)=11$.
$\displaystyle \frac{d}{dx}\pi^2=$
$\pi^2$ is a constant.
Ready for more? Take the Unit 2 test.