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If π¦ = 5(cosΒ² 2π₯ + sinΒ² 2π₯), find dπ¦/dπ₯.

If π¦ is equal to five multiplied by cos squared two π₯ plus sin squared two π₯, find dπ¦ by dπ₯.

In order to work out an expression for dπ¦ by dπ₯, we need to differentiate our equation with respect to π₯. At first glance, this appears quite complicated as we need to differentiate cos squared two π₯ and also sin squared two π₯. However, one of our trigonometric identities states that sin squared π₯ plus cos squared π₯ is equal to one. This also means that sin squared two π₯ plus cos squared two π₯ is also equal to one.

Our equation can be simplified to π¦ is equal to five multiplied by one. Five multiplied by one is equal to five. Therefore, π¦ equals five. We know that differentiating any constant gives us zero. This means that dπ¦ by dπ₯, in this case, equals zero. If π¦ is equal to five multiplied by cos squared two π₯ plus sin squared two π₯, then dπ¦ by dπ₯ equals zero.

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