Video: Finding the First Derivative of a Function Using the Power Rule

Find 𝑑𝑦/𝑑𝑥, given that 𝑦 = 22𝑥⁴.

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Video Transcript

Find 𝑑𝑦 by 𝑑𝑥, given that 𝑦 equals 22𝑥 to the power of four.

If y is equal to 𝑎 multiplied by 𝑥 to the power of 𝑛, then 𝑑𝑦 by 𝑑𝑥 is equal to 𝑛 multiplied by 𝑎 multiplied by 𝑥 to the power of 𝑛 minus one. We multiply the exponent or power by the coefficient and then we subtract one from the exponent.

In our example, as 𝑦 is equal to 22𝑥 to the power of four, then 𝑑𝑦 by 𝑑𝑥 is equal to 88𝑥 to the power of three, as four multiplied by 22 is equal to 88 and four minus one is equal to three. So the new power or exponent is three.

The differential of 𝑦 equals 22𝑥 to the power of four is 88𝑥 cubed or 88𝑥 to the power of three.

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