Blog post #4

Hi, my name is Professor Jordan and I will be explaining derivatives: What they are and how to find them.

Before we start finding derivatives we need to understand why we are finding them. When you find the derivative of an equation at a certain point, you are finding the slope at a certain point of the original equation, which is also the tangent line.

With that explained there are a number of different rules to follow when finding the derivative of specific types of equations.

These rules are:

Constant Function- Used when looking for the derivative of a constant
example:
y=x
d/dx(x)=0

Linear Function- Used for a linear equation in the form y=mx+b
example:
y=4/5x+5
d/dx=4/5+0

A function multiplied by a constant: In this case the derivative of the formula is multiplied by a constant.

Sum & Difference- Used when functions are being added or subtracted
example:
d/dx[f(x)+g(x)]= d/dx(f(x))+ d/dx(g(x))
d/dx[f(x)-g(x)]=d/dx(f(x))- d/dx(g(x))

The Power Rule- Used when the equation is raised to a power

d/dx(x^n)= nX^n-1

example- d/dx (4x^2)= 8x

The Natural Exponent Rule- Used when the equation is a natural number raised to a power

d/dx(e^x)= e^x

example: f(x)= 7e^x-12x---- d/dx=7e^x-(ln12)(12^x)

Derivative of Lnx- Used when find the derivative of a natural log

d/dx (fx)=lnx= 1/x

Product Rule- (f(x) x g(x)) = f(x)` x g(x) + g(x)` x f(x)

Quotient Rule- f(x)/g(x)= f(x)` x g(x) - f(x) x g(x)`/g(x)^2


Its important to remember that each one of these derivative rules find the slope at a certain point specific to the structure of the formula being derived.

Some easy ways to remember these rules:

A constant is always Zero, so: No variable no worries!

The power rule is easy because it is simply a multiplication of its original power and derivative power is only one less number than the original.

Product rule- the derivative of multiplied functions is simply one derivative times  the original of the opposite added together.