Question

differentiate y=2x²+7x²-2/x²-4√x

Answer 1

Answer:

$\bold\red{\frac{dy}{dx} = 18x + \frac{4}{ {x}^{3} } + \frac{2}{ {x}^{ \frac{3}{2} } } }$

Step-by-step explanation:

Given,

$y = 2 {x}^{2} + 7 {x}^{2} - \frac{2}{ {x}^{2} } - \frac{4}{ \sqrt{x} }$

Or we can write it as,

$= > y = 9 {x}^{2} - \frac{2}{ {x}^{2} } - \frac{4}{ \sqrt{x} } \\ \\ = >y = 9 {x}^{2} - 2 {x}^{ - 2} - 4 {x}^{ - \frac{1}{2} }$

Now,

we know that,

$\frac{d}{dx} {x}^{n} = n {x}^{n - 1}$

Therefore,

we get,

$= > \frac{dy}{dx} = 9 \frac{d}{dx} {x}^{2} - 2 \frac{d}{dx} {x}^{ - 2} - 4 \frac{d}{dx} {x}^{ - \frac{1}{2} } \\ \\ = > \frac{dy}{dx} = 18x + 4 {x}^{ - 3} + 2 {x}^{ - \frac{3}{2} } \\ \\ = > \bold{\frac{dy}{dx} = 18x + \frac{4}{ {x}^{3} } + \frac{2}{ {x}^{ \frac{3}{2} } } }$