How do you use the quotient rule to find the derivative of #y=tan(x)# ?

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Answer 1 · 2018-03-06T09:54:18

Kindly refer to the Explanation.

#"The Quotient Rule for Differentiation : "(u/v)'=(vu'-uv')/v^2#.

#:. d/dx(tanx)=(sinx/cosx)'#,

#={cosx*(sinx)'-sinx*(cosx)'}/(csx)^2#,

#={cosx*cosx-sinx(-sinx)}/cos^2x#,

#={cos^2x+sin^2x}/cos^2x#,

#=1/cos^2x#.

# rArr (tanx)'=sec^2x#.