5.6 Derivatives of Polynomials
- Page ID
- 37029
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Given the function f(x) = 6x2 + 3x + 6, find the derivative. When the function is a polynomial, you can find the derivative by doing the following for each term.
f'(x) = 2(6)x2-1 + (1)(3)x0 + (0)6x0-1 = 12x1 + 3x0 + 0 = 12x + 3
1) Bring the exponent down and multiply it by the coefficient.
2) Subtract one from the exponent.
3) Simplify.
4) The derivative of a constant is 0.
Find the derivative of the following polynomial.
f(x) = 4x3 - 5x2 + 10x - 5
Solution
f'(x) = 3(4)x3 - 1 - (2)(5)x2 - 1 + (1)(10)x1 - 1 - 0
f'(x) = 12x2 - 10x1 + 10x0 - 0
f'(x) = 12x2 - 10x + 10