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Question:
differentiate tanx
Answer:

We know that

tanx = sinx/cosx

Now, differentiate w.r.t. x, we get

d(tanx)/dx = d(sinx/cosx)/dx

                = {cosx*cosx - sinx*(-sinx)}/cos2 x

                = {cosx * cosx + sinx*sinx}/cos2 x

                = (cos2 x + sin2 x)/cos2 x

                = 1/cos2 x                          {since cos2 x + sin2 x = 1 }

                = sec2 x

So, d(tanx)/dx = sec2 x

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