Question

Find dy/dx for the given function:y=(x-1)(x-2)/√x

Answer 1

Answer:

Step-by-step explanation:

BRAINLIEST BRAINLIEST BRAINLIEST

Answer 2

Answer:

The equation (iii) is the required answer given below:

Step-by-step explanation:

Provided that:

Given function y = f(x) ;

$y = f(x) = \frac{(x-1)(x-2)}{ \sqrt{x} } \: ...equation(i)$

Simplifying this equation we get;

$y = \frac{(x-1)(x-2)}{ \sqrt{x} } \\ or \: y = \frac{{x }^{2} - 3x + 2}{ {x}^{ \frac{1}{2} } } \\ or \: y = {x}^{ \frac{3}{2} } - 3 {x}^{ \frac{1}{2} } + 2 {x}^{ - \frac{1}{2} } \: ...equation(ii)$

Differentiating equation (ii) with respect to x we get;

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

So, simplifying this equation we get;

$\frac{dy}{dx} = \frac{3}{2} \sqrt{x} - (\frac{3}{2} ) \frac{1}{ \sqrt{x} } - \frac{1}{{x}^{ \frac{3}{2} } } \\ \\ \frac{dy}{dx} = \frac{3}{2} \sqrt{x} - (\frac{3}{2} ) \frac{1}{ \sqrt{x} } - \frac{1}{ \sqrt[3]{x} } \\ \: ...equation(iii)$

So this is the required solution.