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Question
Differentiate the following w.r.t.x:
sin2x2 – cos2x2
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Solution
Let y = sin2x2 – cos2x2
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[sin^2x^2 - cos^2x^2]`
= `"d"/"dx"(sinx^2)^2 - "d"/"dx"(cosx^2)^2`
= `2sinx^2."d"/"dx"(sinx^2) - 2cosx^2."d"/"dx"(cosx^2)`
= `2sinx^2.cosx^2."d"/"dx"(x^2) - 2cosx^2.(-sinx^2)."d"/"dx"(x^2)`
= 2sin x2 . cos x2 x 2x + 2sinx2 . cosx2 x 2x
= 4x (2sinx2 . cosx2)
= 4x sin(2x2).
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