The power rule of calculus is as follows:
The derivative of xn is n*x(n-1)
Note: the derivative of a constant is zero.
This method of differentiation is used for simple polynomials or rational expressions that can be simplified into a single polynomial.
It is also essential to remember the rules of exponents:
https://www.onlinemathlearning.com/exponent-rules.html
Example 1 – find the derivative of f(x)=2x2 + 3x + 4
Let’s apply the power rule to each term in the polynomial:
x2, n = 2:(2)*2x2-1 = 4x1 = 4x
3x, n = 1: (3) * x1-1 = 3x0 = 3 * 1 = 3
4: 0 (4 is a constant, so its derivative is zero)
The derivative of f(x) is f’(x) = 4x+3+0 = 4x+3
Example 2 – find the derivative of f(x) = 
Let’s simplify this term into a single polynomial.
Let’s apply the power rule to each term in the polynomial:
2x2, n = 2:(2)*2x2-1 = 4x1 = 4x
3x1, n = 1:(1)*3x1-1 = 3x0=3 * 1 = 3
4x-2, n = -2:(-2)*4x-2-1 = -8x-3
The derivative of f(x) is f’(x) = 4x+3-8x-3
Example 3 – find the derivative of f(x)= 
at x=3
Let’s simplify this term into a single polynomial.
Let’s apply the power rule to each term in the polynomial:
x, n=1: 1*x1-1=1x0=1*1=1
-3: 0 (since 3 is a constant, the derivative is zero)
The derivative of f(x) is 1 +0 = 1 = f’(x)
Since the derivative is a constant (1), the derivative at any x value is 1.
The graph of the original function proves this:
Example 4 – find the derivative of f(x)=2x-3 + 4x-2 + x-1
Let’s apply the power rule to each term in the polynomial:
Combining the results, the derivative of f(x) is f’(x) = 
