### Video Transcript

Find ππ¦ by ππ₯, given that π¦ is equal to seven π₯ to the power of five plus one divided by π₯ to the power of six.

One divided by π₯ to the power of π is equal to π₯ to the power of negative π. This means that we can rewrite one divided by π₯ to the power of six as π₯ to the power of negative six. If π¦ is equal to π multiplied by π₯ to the power of π, then the differential ππ¦ by ππ₯ is equal to π multiplied by π multiplied by π₯ to the power of π minus one.

Differentiating the first term seven π₯ to the power of five gives us 35π₯ to the power of four, as five multiplied by seven is 35 and reducing the power by one gives us π₯ to the power of four. Differentiating the second term gives us negative six π₯ to the power of negative seven, as negative six minus one is negative seven. The second term can be rewritten as negative six divided by π₯ to the power of seven.

This means that if π¦ is equal to seven π₯ to the power of five plus one divided by π₯ to the power of six, then ππ¦ by ππ₯ is equal to 35π₯ to the power of four minus six divided by π₯ to the power of seven.