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If 𝑦 is equal to five multiplied by cos squared two 𝑥 plus sin squared two 𝑥, find d𝑦 by d𝑥.
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In order to work out an expression for d𝑦 by d𝑥, we need to differentiate our equation with respect to 𝑥.
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At first glance, this appears quite complicated as we need to differentiate cos squared two 𝑥 and also sin squared two 𝑥.
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However, one of our trigonometric identities states that sin squared 𝑥 plus cos squared 𝑥 is equal to one.
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This also means that sin squared two 𝑥 plus cos squared two 𝑥 is also equal to one.
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Our equation can be simplified to 𝑦 is equal to five multiplied by one.
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Five multiplied by one is equal to five.
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Therefore, 𝑦 equals five.
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We know that differentiating any constant gives us zero.
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This means that d𝑦 by d𝑥, in this case, equals zero.
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If 𝑦 is equal to five multiplied by cos squared two 𝑥 plus sin squared two 𝑥, then d𝑦 by d𝑥 equals zero.