Question

Differentiate the function x+2/x-1

Answer 1

Answer:

2x/1x

2x*1x

=2x=2

x=2/2

x=1.ans.

Answer 2

Given :

$\red \bigstar \rm \: differentiate \: the \: function : \\ \color{orange} \star\bf \: \frac{x + 2}{x - 1}$

________________________________________

Formula :

Using Quotient Rule:

Consider a function $\rm{y=\dfrac{v}{x}}$

$\\ \bullet \boxed { \tt{ \: \frac{dy}{dx} = \frac{x \frac{d}{dv}v - v \: \frac{d}{dx}x }{ {x}^{2} } }}$

________________________________________

Solution :

$\\ \implies \sf \: \frac{x + 2}{x - 1} \\ \\ \bf \bullet \: differentiating \: the \: equation \: w.r.t \: to \: x \\ \\ \implies \sf \: y = \frac{x + 2}{x - 1} \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{(x - 1) \frac{d}{dx} (x + 2) - (x + 2) \frac{d}{dx} (x - 1)}{ {(x - 1)}^{2} } \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{(x - 1) \times 1 - (x + 2) \times 1}{ {(x - 1)}^{2} } \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{(x - 1) - (x + 2)}{ {(x - 1)}^{2} } \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{(x - 1 - x - 2)}{ {(x - 1)}^{2} } \\ \\ \\ \implies \sf \: \frac{dy}{dx} = \frac{ - 3}{ {(x - 1)}^{2} } \\ \\ \\ \red \bigstar \boxed{ \sf{ \frac{x + 2}{x -1 } = \frac{ - 3}{ {(x - 1)}^{2} } }}$

Additional information :

$\\ \bullet \tt \: \frac{d}{dx} sinx = cosx$

$\\ \bullet \tt \: \frac{d}{dx} x = 1$

$\\ \bullet \tt \: \frac{d}{dx} \frac{1}{x} = lnx$

$\\ \bullet \tt \: \frac{d}{dx} {e}^{x} = {e}^{x}$

$\\ \bullet \tt \frac{d}{dx} {x}^{2} = 2x$

$\\ \bullet \tt \: \frac{d}{dx} {a}^{x} = {a}^{x} lna$