### Video Transcript

Find ππ¦ by ππ₯, given that π¦ equals 22π₯ to the power of four.

If y is equal to π multiplied by π₯ to the power of π, then ππ¦ by ππ₯ is equal to π multiplied by π multiplied by π₯ to the power of π minus one. We multiply the exponent or power by the coefficient and then we subtract one from the exponent.

In our example, as π¦ is equal to 22π₯ to the power of four, then ππ¦ by ππ₯ is equal to 88π₯ 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 π¦ equals 22π₯ to the power of four is 88π₯ cubed or 88π₯ to the power of three.