Review Elementary Rules of Differentiation

Limit definition of derivative of f(x) at a point:

Derivative of the Constant

Derivative of a Constant Multiple of a function

Assume you have k, which is some number that multiplies a function of x:
The derivative of the constant multiple of a function is the same as the constant multiple of the derivative of that function:

Power Rule

Product Rule

Quotient Rule

Derivative of the Exponential

Derivative of the Natural Logarithm

Derivative of the Sine and Cosine

Practice Exercise: Find the derivative f'(x) of the following

Answer:

Now that we know how to perform some basic differentiation, let's get into what the derivative actually means:
The Derivative in Function Analysis