AP Calculus AB / Unit 2: Differentiation: Definition and Fundamental Properties
2.8 The Product Rule
Notes
$$\frac{d}{dx}[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)$$
Practice
$\displaystyle \frac{d}{dx}(x^2\sin x)=$
First's derivative times second, plus first times second's derivative.
$f(2)=3$, $f'(2)=4$, $g(2)=-1$, $g'(2)=5$. Find $(fg)'(2)$.
$4(-1)+3(5)=11$.
$\displaystyle \frac{d}{dx}(xe^x)=$
$1\cdot e^x+x e^x$.
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