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Question
Differentiate the following w.r.t.x: sec[tan (x4 + 4)]
Solution
Let y = sec[tan (x4 + 4)]
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"{sec[tan(x^4 + 4)]}`
= `sec[tan(x^4 + 4)].tan[tan(x^4 + 4)]."d"/"dx"[tan(x^4 + 4)]`
= `sec[tan(x^4 + 4)].tan[tan(x^4 + 4)].sec^2(x^4 + 4)."d"/"dx"(x^4 + 4)`
= sec[tan(x4 + 4)]·tan[tan(x4 + 4)]·sec2(x4 + 4).(4x3 + 0)
= 4x3·sec2(x4 + 4)·sec[tan(x4 + 4)]·tan[tan(x4 + 4)].
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