Question

differentiate 2x+3/x2-5​

Answer 1

ANSWER:

d/dx [ (2x + 3) / x² - 5 ] = $\frac{ - 2 ( {x}^{2} + 3x + 5) }{ {( {x}^{2} - 5) }^{2} }$

GIVEN:

(2x + 3) / x² - 5

TO FIND:

d/dx [ (2x + 3) / x² - 5 ]

FORMULAE:

d/dx (u/v) = (vu' - uv') ÷ v²

d/dx (x²) = 2x

d/dx (constant) = 0

dx/dx = 1

EXPLANATION:

$\frac{d}{dx} ( \frac{2x + 3}{ {x}^{2} - 5 } ) \\ \\ = \frac{ ({x}^{2} - 5) \frac{d}{dx} (2x + 3) - (2x + 3) \frac{d}{dx}( {x}^{2} - 5) }{ {( {x}^{2} - 5) }^{2} } \\ \\ = \frac{ ({x}^{2} - 5)(2) - (2x + 3) (2x)}{ {( {x}^{2} - 5) }^{2} } \\ \\ = \frac{ 2{x}^{2} - 10 - 4 {x}^{2} - 6x}{ {( {x}^{2} - 5) }^{2} } \\ \\ = \frac{ - 2 {x}^{2} - 6x - 10 }{ {( {x}^{2} - 5) }^{2} } \\ \\ = \frac{ - 2 ( {x}^{2} + 3x + 5) }{ {( {x}^{2} - 5) }^{2} }$

HENCE WE WILL GET,

d/dx [(2x + 3) / x² - 5] = $\frac{ - 2 ( {x}^{2} + 3x + 5) }{ {( {x}^{2} - 5) }^{2} }$

Answer 2

Explanation:

The answer is written in the above attachment...