Derivatives
The derivative is the slope of the tangent, and the rate at which a quantity is changing.
A worked example
For f(x) = 2x⁵ − 4x³, the power rule gives f′(x) = 10x⁴ − 12x². At x = 1 that is −2.
The mistake people actually make
With the chain rule, do not forget to multiply by the derivative of the inside function.