Derivative of Polynomial Function
Input polynomial function
f(x) =

Derivative Of Product of Polynomial Functions

( )•

( )

Derivative of Quotient of Polynomial Functions

Difference Quotient for Polynomial Function
Use Δx notation       Use 'h' notation

Input function f(x) =

Partial Fraction Decomposition

Difference Quotient for Square Root Function          Use Δx notation       Use 'h' notation

Input function f(x) = √

Adding, Subtracting, Multiplying, and Simplifying Polynomial Expressions
For division of polynomials, use "÷" ; Example: (5x² - 3x - 1)÷(2x+6)

Input Polynomial Expression =

Dividing Two Polynomials

     
^{______________________________________________________________________}
     

Composing Polynomial Functions: (f o g)(x) or (g o f)(x)

Input f(x) =

Input g(x) =

Adding/Subtracting/Multiplying/Dividing Two Rational Expressions

	+

    

Adding/Subtracting/Multiplying/Dividing Three Rational Expressions

	+		+

    

outputdiv2

f(x) = √

f(x + Δx ) = √

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The Difference Quotient:

f(x + Δx) - f(x)

Δx

=  

√       -   √

Δx

=  

(√       -   √     )	(√       +   √     )
Δx	(√       +   √     )

=  

Δx(√       +   √     )

=  

Δx(√       +   √     )

=  

(√       +   √     )

Operations of Rational Expressions

   

111111111111	+	222222222222222
333333333		5555555

=	111111111111
	333333333

=	111111111111
	333333333

=	111111111111
	333333333

=	boxk11bb
	boxk1bb

Partial Fraction Decomposition

Result of polynomial factoring

outputdiv2