Question

find dy/dx for the following function
pls help me..........
class 11 physics
no irrelevant answers plz..​

Answer 1

Answer:

$y = \dfrac{(x - 1)(x - 2)}{ \sqrt{x} }$

$= > y = \dfrac{ {x}^{2} - 3x + 2 }{ \sqrt{x} }$

Dividing the numerator term by denominator , we get :

$= > y = {x}^{ \frac{3}{2} } - 3 \sqrt{x} + 2 {x}^{ (- \frac{1}{2} )}$

Now apply simple differentiation technique after this step :

$= > \dfrac{dy}{dx} = \dfrac{d {(x)}^{ \frac{3}{2} } }{dx} - 3\dfrac{d( {x}^{ \frac{1}{2} } )}{dx} + 2\dfrac{d( {x}^{ - \frac{1}{2} } )}{dx}$

$= > \dfrac{dy}{dx} = \dfrac{3}{2} \sqrt{x} - \dfrac{3}{2} \dfrac{1}{ \sqrt{x} } + ( - \dfrac{2}{2} ) \dfrac{1}{ {x}^{ \frac{3}{2} } }$

$= > \dfrac{dy}{dx} = \dfrac{3}{2} \sqrt{x} - \dfrac{3}{2} \dfrac{1}{ \sqrt{x} } - \dfrac{1}{ {x}^{ \frac{3}{2} } }$

Basic formula is :

$\bigstar \: \: y = {x}^{n}$

$= > \dfrac{dy}{dx} = n {x}^{(n - 1)}$