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, start superscript, 2, end superscript, minus, 2, x, plus, 1 for example.
=ddx(3x22x+1)=3ddx(x2)2ddx(x)+ddx(1)=3(2x)2(1)+(0)=6x2\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, start superscript, 3, end superscript, minus, x, start superscript, 2, end superscript
f, prime, left parenthesis, x, right parenthesis, equals

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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, start superscript, 3, end superscript, minus, x, start superscript, 2, end superscript
f, prime, left parenthesis, 2, right parenthesis, equals, question mark
Please choose from one of the following options.

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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, start superscript, 2, end superscript at the point where x, equals, 1.
Please choose from one of the following options.

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Practice set 4: Find normal line equations

Problem 4.1
Find an equation of the line normal to the graph of g, left parenthesis, x, right parenthesis, equals, x, start superscript, 3, end superscript, minus, 5, x, start superscript, 2, end superscript, plus, 10 at the point where x, equals, 2.
Please choose from one of the following options.