Question

find the differentiation of (9.) y = (x ^ 2 + 1)[x + 5 + 1/x]​

Answer 1

$\sf\pink{dy = d[(x² + 1) × ( x +5 + \dfrac{1}{x}]}$

${\sf\green{\underline{\underline{By\: using\: Product\: rule : }}}}$

$\sf\blue{\fbox{d(u.v) = ud(v) + vd(u)}}$

$\sf\orange{dy = d[(x² + 1) × ( x +5 + \dfrac{1}{x})]}$

$\small\sf{=> [( x² + 1 ) d(x+5+x^{-1})] + [(x+5+x^{-1}) d(x²+1)]}$

$\sf\orange{=> x² + 1 (1-x^{-2}) + (x+5+x^{-1}).2x}$

$\sf\orange{=> (x²+1)(1-\dfrac{1}{x²}) + 2x(x+5+x^{-1})}$