\[\begin{aligned}
P(x) &= a_0+a_1x+a_2x^2+\cdots+a_nx^n \\
P'(x) &= a_1+2a_2x+3a_3x^2+\cdots+na_nx^{n-1}
\end{aligned}\]
Variables
dPderivative value of the polynomial
xevaluation variable
a1linear coefficient
a2quadratic coefficient
a3cubic coefficient
a4quartic coefficient
a5quintic coefficient
Description
What is this formula?
This formula calculates the derivative of a polynomial at a specific value of x. The derivative represents the instantaneous rate of change or slope of the polynomial function.
When to use it
Use this formula when determining slopes, rates of change, optimization conditions or analyzing polynomial behavior.
Example
For:
P(x)=2+(3*x)+(4*x²)
Its derivative is:
dP=3+(2*4*x)
If x=2:
dP=3+(8*2)
dP=19
Applications
Optimization problems
Engineering analysis
Motion equations
Numerical methods
Curve analysis
Scientific computing