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D(1/(sinx))=...

`D(1/(sinx))=`

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If (d)/(dx)((x)/(sinx))=

(d)/(dx)((cosx)/(1+sinx))=

(d)/(dx)[tan^(-1)sqrt((1+sinx)/(1-sinx))]=

(d)/(dx)[log(sqrt((1+sinx)/(1-sinx)))]=

(d)/(dx)(sin{2cos^(-1)(sinx)}]=

(d)/(dx)((cosx+sinx)/(cosx-sinx))=

At x=(pi)/(4),(d)/(dx)[tan^(-1)((cosx)/(1+sinx))]=

d/(dx)(tan^(-1) ((cos x)/(1+sinx)) =

(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))=? (x is in IV quadrant)

Differentiate the following w.r.t. x : cos^(-1)(sinx)