Basic rules
Computing every derivative from the limit definition would be slow. A handful of rules covers almost every function you'll meet.
Derivatives of common functions
\(e^x\) is its own derivative, which is what makes \(e\) the "natural" base.
Product and quotient rules
The chain rule
For a composition \(f(g(x))\):
Higher derivatives
The derivative of \(f'\) is the second derivative \(f''\), or \(\frac{d^2y}{dx^2}\). If \(s(t)\) is position, \(s''(t)\) is acceleration.
Practice
Quick check
What is \(\frac{d}{dx}[\sin 2x]\)?
Chain rule: the derivative of the inside, \(2\), multiplies \(\cos 2x\).
Quick check
What is \(\frac{d}{dx}[\ln x]\)?
The natural log has derivative \(\frac{1}{x}\).