Video: Differentiating Polynomials

Evaluate 𝑑/𝑑𝑥 (−3𝑥² − 4𝑥 + 5).

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Video Transcript

Evaluate 𝑑 by 𝑑𝑥 of negative three 𝑥 squared minus four 𝑥 plus five.

In order to differentiate any term 𝑎 multiplied by 𝑥 to the power of 𝑛, we multiply the power by the coefficient and decrease the power by one. Therefore, 𝑑𝑦 by 𝑑𝑥 is equal to 𝑛 multiplied by 𝑎 multiplied by 𝑥 to the power of 𝑛 minus one. In this case, we will let 𝑦 be the expression negative three 𝑥 squared minus four 𝑥 plus five.

Differentiating the first term negative three 𝑥 squared gives us negative six 𝑥 as two multiplied by negative three is negative six and decreasing the power by one gives us 𝑥 to the power of one or 𝑥.

Differentiating the second term, negative four 𝑥 or negative four 𝑥 to the power of one gives us negative four. One multiplied by negative four is negative four. When we decrease the power, we get 𝑥 to the power of zero. And anything to the power of zero is equal to one.

Finally, differentiating any constant gives us zero. Therefore, the differential of positive five is zero.

This means that the differential of negative three 𝑥 squared minus four 𝑥 plus five is negative six 𝑥 minus four.

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