Calculus I
&
Engineering Mathematics 2
Workshop 3
Definition: The derivative of a function $f(x)$ is defined as
\(\ds f'(x) = \lim_{h\to 0}\frac{f(x+h) - f(x)}{h}\)
Derivative Rules
| Rule | Function | Derivative |
| Product Rule | \( y = u \cdot v \) | \( \dfrac{dy}{dx} = u'v + uv' \) |
| Quotient Rule | \( y = \dfrac{u}{v} ,\,\) \(v\neq 0\) | \( \dfrac{dy}{dx} = \dfrac{u'v - uv'}{v^2} \) |
| Chain Rule | \( y = f(u), \; u = g(x) \) | \( \dfrac{dy}{dx} = \dfrac{dy}{du}\cdot\dfrac{du}{dx} \) |