Question

how d(tanx)/dx = sec^2x

Answer 1

Here is your Answer!
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d/dxtan(x) = d/dx sin(x)/cos(x)

= ( cos(x) d/dx sin(x) - sin(x) d/dx cos(x) ) / cos^2(x)

= [ ( cos(x)cos(x) + sin(x)sin(x) ) ]/ cos^2(x)

= 1 + tan^2(x) = sec^2(x)   Ans!