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## Calculus, all content (2017 edition)

### Unit 2: Lesson 13

Polynomial functions differentiation

# Differentiating polynomials review

Review your polynomial differentiation skills and use them to solve problems.

## How do I differentiate polynomials?

To differentiate polynomials, all you need are the Power rule and the basic differentiation rules. Let's differentiate 3, x, squared, minus, 2, x, plus, 1 for example.
\begin{aligned} &\phantom{=}\dfrac{d}{dx}(3x^2-2x+1) \\\\ &=3\dfrac{d}{dx}(x^2)-2\dfrac{d}{dx}(x)+\dfrac{d}{dx}(1) \\\\ &=3(2x)-2(1)+(0) \\\\ &=6x-2 \end{aligned}
Want a deeper explanation of differentiating polynomials? Check out this video.

## Practice set 1: Differentiate polynomials

Problem 1.1
f, left parenthesis, x, right parenthesis, equals, x, start superscript, 5, end superscript, plus, 2, x, cubed, minus, x, squared
f, prime, left parenthesis, x, right parenthesis, equals

Want to try more problems like this? Check out this exercise.

## Practice set 2: Evaluate polynomial derivatives

Problem 2.1
f, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, plus, 3, x, cubed, minus, x, squared
f, prime, left parenthesis, 2, right parenthesis, equals, question mark

Want to try more problems like this? Check out this exercise.

## Practice set 3: Find tangent equations

Problem 3.1
Find an equation of the line tangent to the graph of f, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, plus, 2, x, squared at the point where x, equals, 1.