What is the derivative of (-u^2+3)/((u^2+3)^2) ?

The derivative of (-u^2+3)/((u^2+3)^2) is -(2u(-u^2+9))/((u^2+3)^3)

What is the first derivative of (-u^2+3)/((u^2+3)^2) ?

The first derivative of (-u^2+3)/((u^2+3)^2) is -(2u(-u^2+9))/((u^2+3)^3)

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derivative of

\frac{- u ^{2} + 3}{( u ^{2} + 3 ) ^{2}}

- \frac{2 u ( - u ^{2} + 9 )}{( u ^{2} + 3 ) ^{3}}

Solution steps

\frac{d}{d u} (\frac{- u ^{2} + 3}{( u ^{2} + 3 ) ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d u} ( - u ^{2} + 3 ) ( u ^{2} + 3 ) ^{2} - \frac{d}{d u} ( ( u ^{2} + 3 ) ^{2} ) ( - u ^{2} + 3 )}{( ( u ^{2} + 3 ) ^{2} ) ^{2}}

\frac{d}{d u} (- u^{2} + 3) = - 2 u

\frac{d}{d u} ((u^{2} + 3)^{2}) = 4 u (u^{2} + 3)

= \frac{( - 2 u ) ( u ^{2} + 3 ) ^{2} - 4 u ( u ^{2} + 3 ) ( - u ^{2} + 3 )}{( ( u ^{2} + 3 ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 u ) ( u ^{2} + 3 ) ^{2} - 4 u ( u ^{2} + 3 ) ( - u ^{2} + 3 )}{( ( u ^{2} + 3 ) ^{2} ) ^{2}} : - \frac{2 u ( - u ^{2} + 9 )}{( u ^{2} + 3 ) ^{3}}

= - \frac{2 u ( - u ^{2} + 9 )}{( u ^{2} + 3 ) ^{3}}

What is the derivative of (-u^2+3)/((u^2+3)^2) ?
The derivative of (-u^2+3)/((u^2+3)^2) is -(2u(-u^2+9))/((u^2+3)^3)
What is the first derivative of (-u^2+3)/((u^2+3)^2) ?
The first derivative of (-u^2+3)/((u^2+3)^2) is -(2u(-u^2+9))/((u^2+3)^3)