Question

Find the derivative of tan x with respect to x using quotient rule​

Answer 1

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Using the quotient rule it is easy to obtain an expression for the derivative of tangent: (tanx)′=(sinxcosx)′=(sinx)′cosx−sinx(cosx)′cos2x=cosx⋅cosx−sinx⋅(−sinx)cos2x=cos2x+sin2xcos2x=1cos2x. The derivative of cotangent can be found in the same way. ... (cscx)′=(1sinx)′=−1sin2x⋅(sinx)′=−cosxsin2x=−cosxsinx⋅1sinx=−cotxcscx.

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