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Question
Differentiate the following:
y = sin3x + cos3x
Solution
y = sin3x + cos3x
Here u = sin3x = (sin x)3
⇒ `("d"u)/("d"x)` = 3(sin x)2(cos x)
= 3sin2x cosx
v = cos3x = (cos x)3
⇒ `("d"u)/("d"x)` = 3(cos x)2 (– sin x)
= – 3 sin x cos2x
Now y = u + v
⇒ `("d"y)/("d"x) = ("d"u)/("d"x) + ("d"v)/("d"x)`
= 3 sin2x cos x – 3sin x cos2x
= 3 sin x cos x (sin x – cos x)
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