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Question
Differentiate the following w.r.t. x : `"cosec"^-1[1/cos(5^x)]`
Solution
Let y = `"cosec"^-1[1/cos(5^x)]`
= cosec–1[sec(5x)]
= `"cosec"^-1["cosec"(pi/2 - 5^x)]`
= `pi/(2) - 5^x`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"(pi/2 - 5^x)`
= `"d"/"dx"(pi/2) - "d"/"dx"(5^x)`
= 0 –5x.log5
= –5x.log5.
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