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Differentiate the following functions wi...

Differentiate the following functions with respect to `x` : `tan^(-1){sqrt((1+sinx)/(1-sinx))}`

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y=`tan^(-1){sqrt((1+sinx)/(1-sinx))}`
=`tan^(-1){sqrt((1+2sin(x/2)cos(x/2))/(1-2sin(x/2)cos(x/2)))}`
=`tan^(-1){sqrt((cos^2(x/2)+sin^2(x/2)+2sin(x/2)cos(x/2))/(cos^2(x/2)+sin^2(x/2)-2sin(x/2)cos(x/2)))}`
=`tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))`
=`tan^(-1)((1+tan(x/2))/(1-tan(x/2)))`
=`tan^(-1)tan(pi/4+x/2)`
`dy/dx=1/2`
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  15. Differentiate e^(sqrt(x)) with respect to x from first-principles

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