AP Calculus AB / Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
3.1 The Chain Rule
Notes
$$\frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)$$
- Differentiate the outside, keep the inside, then multiply by the inside's derivative.
Practice
$\displaystyle \frac{d}{dx}(3x+1)^5=$
Outside: $5u^4$; inside derivative: 3.
$\displaystyle \frac{d}{dx}\sin(x^2)=$
Multiply by the derivative of $x^2$.
$\displaystyle \frac{d}{dx}e^{4x}=$
The inside $4x$ has derivative 4.
Ready for more? Take the Unit 3 test.