Remember that the derivative is defined as the instantaneous rate of change of a function. We can go back to the fundamental definition and "derive" the derivative in each and every case. This would be cumbersome. Fortunately,  there are differentiation rules that can be used. Together with the general rules from the previous page we can now calculate the derivative for a large amount of functions and/or combinations and compositions of functions. Here are some of the quick rules: 
Recall, these rules only apply to the functions in their basic, elementary standard form.
d/dx c = 0

The derivative of a constant is zero. 
Example: d/dx 7 = 0

d/dx c × x = c

The rate of change of a linear function is its slope. 
Example: d/dx 3 × x = 3

d/dx (xn) = n × x(n-1)

	Example: d/dx (x4) = 4 × x 3

d/dx ln|x|= 1/x

The derivative of the natural log of x is its inverse. 

d/dx (eax) = a eax

Example: d/dx (e3x) = 3 e3x

d/dx (ax) = ax ln(a)

	Example: d/dx (3x) = 3x ln(3)

d/dx (sin x) = cos x

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

d/dx (cos x) = -sin x

Example: dy/dx (cos x) = - sin x

d/dx (sec x) = sec x tan x

d/dx (tan x) = (sec x )^2 

By using the derivative rules in combination, we can find the derivatives of many other functions.