Question

(x^2+1)^2(x+1)^-3 , differentiate with respect to x

Answer 1

Given that ,differentiate with respect to X

Answer 2

Answer :



$( {x}^{2} + 1) {}^{2} (x + 1) {}^{ - 3} \\ \\ express \: with \: positive \: exponent \: by \: using \\ \\ a {}^{ - n} = \frac{1}{a {}^{n} } \\ \\ ( {x}^{2} + {1})^{2} \times \frac{1}{ {(x + 1)}^{3} } \\ \\ \frac{( {x}^{2} + {1) }^{2} \times 1}{ {(x + 1)}^{3} } \\ \\ \frac{( {x}^{2} + 1) {}^{2} }{ {(x + 1)}^{3} }$
$use \: \: the \: \: identity \: \: \\ ( {a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} \\ and \: expand \: the \: expression \\ \\ \frac{( {x}^{2} {)}^{2} + 2 {x}^{2} \times 1 + {1}^{2} }{( {x + 1)}^{3} } \\ \\ \frac{ {x}^{4} + {2x}^{2} + 1 }{(x + 1) {}^{3} } \:$