# Unit 15

Calculus: Basic differentiation an introduction:

More practice of basic differentiation:

Fractional and negative powers:

Finding the equation of a tangent line and normals:

Increasing and decreasing functions:

Differentiation from first principles:

Differentiating e^x

Product rule 1:

Product rule 2:

Quotient Rule 1:

Quotient Rule 2:

Chain rule for brackets:

Chain rule for e^x:

Product rule and chain rule:

Quotient rule and chain rule:

Chain rule for lnx:

Differentiating trig:

The first derivative test to find max, min:

The second derivative test to find max, min:

Optimisation problems:

More difficult optimisation problems:

An introduction to kinematics (speed, distance, acceleration):

More on Kinematics (including integration)

Introduction to basic integration:

Integrating fractional powers:

The fundamental theorem of calculus – how to find definite integrals:

Finding the areas under graphs:

Integrating e^x:

Integrating sinx and cosx (ignore sec x, cosec x and tanx integrals):

Integrating functions of the form (ax + b)^n by inspection:

Velocity time graphs:

Using integration for kinematics problems:

Finding the area between 2 curves:

An Excellent Calculus Playlist: