What is Differentiation ?

Given a function and a specific point, the differentiation at that point is the slope of a tangent line at that point.
If f(x) is the original function, then the differentiation of f is f'(x) (pronounced f prime) or df/dx


The derivative is sometimes called the slope of the tangent line to the graph at a particular point.


The differentation is also commonly called the derivative



First Principals

This deriavative is a linear operator that inputs a function and returns another function.
This is in contrast to an algebraic equation that inputs a number and returns another number.







Leibniz Notation

dx




Straight Lines


y = mx + c




Polynomials


A line through 2 points on a curve is called a secant line


example - x squared
derivative is 2x



example - x cubed - x squared + 4x -3



Two Functions




Derivative of Ln




Derivative of Ln with functional argument





Rules

 




Examples



Derivative of e


 



Derivative of e with functional argument

The derivative of e with a functional exponent is equal to e with that derivative of that exponent.
We can use the chain rule here because we have a composite function.


 




Examples

 




Logarithms



Rules

 


Examples



Trigonometric



Examples



Inverse



© 2018 Better Solutions Limited. All Rights Reserved. © 2018 Better Solutions Limited TopPrevNext