How to find a derivative
- Type the function of x, such as x^3 + 2x, sin(x)·e^x or ln(x^2 + 1).
- Choose first or a higher derivative, and optionally a point to evaluate it at.
- Read the derivative and the rules used: power, product, quotient, chain and so on.
Common derivatives
| f(x) | f′(x) |
|---|---|
| xⁿ | nxⁿ⁻¹ |
| eˣ | eˣ |
| aˣ | aˣ ln a |
| ln x | 1/x |
| sin x | cos x |
| cos x | −sin x |
| tan x | 1/cos²x |
| √x | 1/(2√x) |
What a derivative tells you
The derivative is the slope of the function at each point: how fast it is changing. Where it is 0 the graph is flat, which is how maximums and minimums are found. In physics, the derivative of position over time is velocity, and of velocity is acceleration.