What is the derivative of $f(x)=tan(x)cot(x)$ ?

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Answer 1 · 2016-05-05T15:17:15

$(df(x))/dx=0$

As $f(x)=tanx*cotx=1$ , $(df(x))/dx=0$ .

However, let us also try using product rule.

$df(x)/dx=cotxd/dx(tanx)+tanxd/dx(cotx)$

= $cotx*sec^2x+tanx*(-csc^2x)$

= $cosx/sinx*1/cos^2x-sinx/cosx*1/sin^2x$

= $1/(sinxcosx)-1/(sinxcosx)=0$

What is the derivative of f(x)=tan(x)cot(x) f(x)=tan(x)cot(x)?