Question

differentiate y=1/x+2with respect to x.

Answer 1

$y = \frac{1}{x + 2} \\ \\ differentiate \: it \: using \: quotient \: rule. \: w.r.t \: \: \: x \: \: \: \\ \\ \frac{dy}{dx} = \frac{ ({x}^{2} + 2 ) \times \frac{d(1)}{dx} - 1 \times \frac{d( {x}^{2} + 2) }{dx} }{ {( {x}^{2} + 2) }^{2} } \\ = > \frac{ - 2x}{ {( {x}^{2} + 2) }^{2} }$
Formulas Used :-
d
$1) \: \: \: \frac{d {x}^{n} }{dx} = n {x}^{n -1} \\ \\ 2) \: \: \: \frac{d(c)}{dx} = 0 \\ where \: c \: can \: be\: any \: constant$