[Calculus] Quick Review for Tutorial 5

1. Definition of differentiation
We say f is differentiate at $c$ if $lim_{x\rightarrow c} {f(x)-f(c) \over x-c}$ exists.

2. Differentiation Rules
$$(\alpha f(x) + \beta g(x))\prime=\alpha f\prime(x) + \beta g\prime(x)$$
$$(f(x)g(x))\prime = f\prime(x)g(x) + f(x)g\prime (x)$$
$$({f(x) \over g(x)})\prime = {f(\prime x)g(x)-f(x)g\prime (x) \over (g(x))^{2}}$$
$$(fg(x))\prime(x)=f\prime(g(x))g\prime(x)$$

3. Implicit Differentiation

4. Differentiation of Inverse Function
$$(f^{-1})(x) = {1 \over f\prime (y)} = {1 \over f\prime(f^{-1}(x))}$$