Question

Differentiate (5x^4-7x^3+2x^2+x-3)/x^2​

Answer 1

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$\mapsto \sf y = \frac{5 {x}^{4} - 7 {x}^{3} + {2x}^{2} + x - 3}{ {x}^{2} }$

$\mapsto \sf y = \frac{5 {x}^{4} }{ {x}^{2} } - \frac{7 {x}^{3} }{ {x}^{2}} + \frac{ {2x}^{2} }{ {x}^{2} } + \frac{x}{ {x}^{2} } - \frac{3}{ {x}^{2}}$

$\mapsto \sf y = 5 {x}^{2} - 7x + 2 + \frac{1}{x} - \frac{3}{ {x}^{2} }$

$\mapsto\boxed{ \sf \frac{dy}{dx} = 10x - 7 + \frac{1}{ {x}^{2} } - \frac{3}{ {x}^{3} }}$