Question:
Compute the derivative of tan x.
Answer:
tan x = sin x/cos x
Now d(tan x)/dx = d(sin x/cos x)/dx
= {cos x * d(sin x)/dx - sin x * d(cos x)/dx}/cos2 x
= {cos x * cos x + sin x * sin x}/cos2 x
= (cos2 x + sin2 x)/cos2 x {since cos2 x + sin2 x = 1}
= 1/cos2 x
= sec2 x
So, d(tan x)/dx = sec2 x
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