Derivatives of some common functions

Fortunately, we don't have to follow the steps on the previous page in order to differentiate most functions since there are differentiation rules that can be used.

dy/dx c = 0

The derivative of a constant is zero.

Example: dy/dx 7 = 0

dy/dx c × x = c

The rate of change of a linear function is its slope.

Example: dy/dx 3 × x = 3

dy/dx (xⁿ) = n × x^(n-1)

Example: dy/dx (x⁴) = 4 × x ³

dy/dx (log x) = 1/x

The derivative of the log of x is its inverse.

Example: dy/dx (log (x + 1)) = 1 / (x + 1)

dy/dx (e^ax) = a e^ax

Example: dy/dx (e^3x) = 3 e^3x

dy/dx (sin x) = cos x

Example: dy/dx (sin y) = cos y

dy/dx (cos x) = -sin x

Example: dy/dx (cos ) = - sin

Do you want to see the graphs of the derivatives of a few functions?
Graphing interactive workbench