Question

(dy/dx)=y=(x+1)/(x+2)^(3))​

Answer 1

We have,

$\boxed{y = \dfrac{(x + 1) \: \: }{ {(x + 2)}^{3} } }$

Thus,

$\quad \: \sf \dfrac{dy}{dx} \\ \\ = \frac{ \sf{d} \left( \dfrac{(x + 1)}{ {(x + 2)}^{3} } \right)}{ \sf{d}y} \\ \\ = \lim _{\Delta x \to 0} \dfrac{f(x + \Delta x ) - f(x)}{ \Delta x} \\ \\ = \lim _{\Delta x \to 0} \dfrac{ \dfrac{(x + \Delta x + 1)}{ {( x + \Delta x + 2)}^{3} } - \dfrac{(x+1)}{ {(x + 2)}^{3} }}{ \Delta x}$