Réitigh fy=tanx.u=v-1/v.text{and}v=lnx.text{whatisthevalueof}dy/dxtext{at}x=e?

$$f y = \tan x . u = v - \frac { 1 } { v } . \text { and } v = \ln x . \text { what is the value of } \frac { d y } { d x } \text { at } x = e ?$$

Réitigh do f. (complex solution)

$$\left\{\begin{matrix}f=\frac{\tan(x)}{y}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }y\neq 0\\f\in \mathrm{C}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}\text{ and }y=0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Tá an chothromóid i bhfoirm chaighdeánach.

$$yf=\tan(x)$$

Roinn an dá thaobh faoi y.

$$\frac{yf}{y}=\frac{\tan(x)}{y}$$

Má roinntear é faoi y cuirtear an iolrúchán faoi y ar ceal.

$$f=\frac{\tan(x)}{y}$$

Réitigh do f.

$$\left\{\begin{matrix}f=\frac{\tan(x)}{y}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}\text{ and }y\neq 0\\f\in \mathrm{R}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }x=\pi n_{2}\text{ and }y=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Tá an chothromóid i bhfoirm chaighdeánach.

$$yf=\tan(x)$$

Roinn an dá thaobh faoi y.

$$\frac{yf}{y}=\frac{\tan(x)}{y}$$

Má roinntear é faoi y cuirtear an iolrúchán faoi y ar ceal.

$$f=\frac{\tan(x)}{y}$$