How to Differentiate Polynomials

Step-by-Step Guide

1. 1

   Step 1: Identify the variable terms and constant terms in the equation.

   A variable term is any term that includes a variable and a constant term is any term that has only a number without a variable.
   
   Find the variable and constant terms in this polynomial function: y = 5x3 + 9x2 + 7x + 3 The variable terms are 5x3, 9x2, and 7x The constant term is 3
2. 2

   Step 2: Multiply the coefficients of each variable term by their respective exponents.

   Their products will form the new coefficients of the differentiated equation.
   
   Once you find their products, place the results in front of their respective variables.
   
   Here's how you do it: 5x3 = 5 x 3 = 15 9x2 = 9 x 2 = 18 7x = 7 x 1 = 7 , To do this, simply subtract 1 from each exponent in each variable term.
   
   Here's how you do it: 5x3 = 5x2 9x2 = 9x1 7x = 7 , To finish differentiating the polynomial equation, simply replace the old coefficients with their new coefficients and replace the old exponents with their values lowered by one degree.
   
   The derivative of constants is zero so you can omit 3, the constant term, from the final result. 5x3 becomes 15x2 9x2 becomes 18x 7x becomes 7 The derivative of the polynomial y = 5x3 + 9x2 + 7x + 3 is y = 15x2 + 18x + 7 , To find the value of "y" with a given "x," simply replace all of the "x"s in the equation with the given value of "x" and solve.
   
   For example, if you want to find the value of the equation at x = 2, simply plug the number 2 in place of every x in the equation.
   
   Here's how to do it: 2
   --> y = 15x2 + 18x+ 7 = 15 x 22 + 18 x 2 + 7 = y = 60 + 36 + 7 = 103 The value of the equation at x = 2 is
   103.
3. 3

   Step 3: Lower each exponent by one degree.

4. 4

   Step 4: Replace the old coefficients and old exponents with their new counterparts.

5. 5

   Step 5: Find the value of the new equation with a given "x" value.

Detailed Guide

About the Author