Question

differentiate a*2+x*2/a*2-x*2​

Answer 1

Hey There

Here's The Answer

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Answer 2

Solution:-

$\to \rm \: \dfrac{d}{dx} \bigg(\dfrac{ {a}^{2} + {x}^{2} }{ {a}^{2} - {x}^{2} } \bigg)$

Using U/V method

$\boxed{ \rm \: \dfrac{d}{dx} \bigg( \dfrac{u}{v} \bigg) = \dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx} }{ {v}^{2} } }$

Now using this method:-

$\rm \to \: \dfrac{d}{dx} \bigg(\dfrac{ {a}^{2} + {x}^{2} }{ {a}^{2} - {x}^{2} } \bigg) = \dfrac{( {a}^{2} - x {}^{2} ) \times 2x - (a {}^{2} + {x}^{2} ) \times - 2x }{( {a}^{2} - {x}^{2} )^{2} }$

$\rm = \dfrac{( {a}^{2} - x {}^{2} ) \times 2x + (a {}^{2} + {x}^{2} ) \times 2x }{( {a}^{2} - {x}^{2} )^{2} }$

$= \rm \: \dfrac{2x {a}^{2} - 2 {x}^{3} + 2x {a}^{2} + 2 {x}^{3} }{( {a}^{2} - {x}^{2} ) {}^{2} }$

$= \rm \: \dfrac{2x {a}^{2} - \cancel{2 {x}^{3} } + 2x {a}^{2} + \cancel{ 2 {x}^{3}} }{( {a}^{2} - {x}^{2} ) {}^{2} }$

$= \rm \: \dfrac{4x {a}^{2} }{( {a}^{2} - {x}^{2} ) ^{2} }$

Answer is

$= \rm \: \dfrac{4x {a}^{2} }{( {a}^{2} - {x}^{2} ) ^{2} }$