Question

plz solve this from differentiation ​

Answer 1

Step-by-step explanation:

d(x³+1/x³-1)

(x³-1)(3x²)-(x³+1)(3x²) / (x³-1)²

3x²(x³-1-x³-1) / (x³-1)²

-6x² / (x³-1)²

Answer 2

$\huge \: \mathfrak{solution}$

To Differentiate :

$\star \: \frac{ {x}^{3} + 1 }{ {x}^{3} - 1 }$

Here we use the formula :

$\boxed{ \bold{\frac{d}{dx} ( \frac{u}{v} ) = \frac{v \: \frac{d}{dx}(u) - u \: \frac{d}{dx}(v) }{ {v}^{2} } }}$

$\star \: \frac{d}{dx} ( \frac{ {x}^{3} + 1 }{ {x}^{3 } - 1 } ) \\ \\ \star \: \frac{ ({x}^{3} - 1 )\frac{d}{dx}( {x}^{3} + 1) - ({x}^{3} + 1) \frac{d}{dx}( {x}^{3} - 1) }{( {x}^{3} - 1) ^{2} } \\ \\ \star \frac{( {x}^{3} - 1)(3 {x}^{2} + 0) - ( {x}^{3} + 1)(3 {x}^{2} - 0) }{( {x}^{3} - 1) ^{2} } \\ \\ \star \: \frac{(3 {x}^{5} + 0 - 3 {x}^{2} - 0) - (3 {x}^{5} - 0 + 3 {x}^{2} - 0) }{( {x}^{3} - 1) ^{2} } \\ \\ \star \: \frac{ \cancel{3 {x}^{5}} - 3 {x}^{2} - \cancel{3 {x}^{5} } - 3 {x}^{2} }{( {x}^{3} - 1)^{2} } \\ \\ \star \: \frac{ - 6 {x}^{2} }{( {x}^{3} - 1) ^{2} }$