What is the derivative of (-u^2+8)/((u^2+8)^2) ?

The derivative of (-u^2+8)/((u^2+8)^2) is -(2u(-u^2+24))/((u^2+8)^3)

What is the first derivative of (-u^2+8)/((u^2+8)^2) ?

The first derivative of (-u^2+8)/((u^2+8)^2) is -(2u(-u^2+24))/((u^2+8)^3)

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derivative of

\frac{- u ^{2} + 8}{( u ^{2} + 8 ) ^{2}}

- \frac{2 u ( - u ^{2} + 24 )}{( u ^{2} + 8 ) ^{3}}

Solution steps

\frac{d}{d u} (\frac{- u ^{2} + 8}{( u ^{2} + 8 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d u} ( - u ^{2} + 8 ) ( u ^{2} + 8 ) ^{2} - \frac{d}{d u} ( ( u ^{2} + 8 ) ^{2} ) ( - u ^{2} + 8 )}{( ( u ^{2} + 8 ) ^{2} ) ^{2}}

\frac{d}{d u} (- u^{2} + 8) = - 2 u

\frac{d}{d u} ((u^{2} + 8)^{2}) = 4 u (u^{2} + 8)

= \frac{( - 2 u ) ( u ^{2} + 8 ) ^{2} - 4 u ( u ^{2} + 8 ) ( - u ^{2} + 8 )}{( ( u ^{2} + 8 ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 u ) ( u ^{2} + 8 ) ^{2} - 4 u ( u ^{2} + 8 ) ( - u ^{2} + 8 )}{( ( u ^{2} + 8 ) ^{2} ) ^{2}} : - \frac{2 u ( - u ^{2} + 24 )}{( u ^{2} + 8 ) ^{3}}

= - \frac{2 u ( - u ^{2} + 24 )}{( u ^{2} + 8 ) ^{3}}

f (x) = e^{x} cosh (x)

x^{2} y^{^{''}} - 11 x y^{^{'}} + 36 y = 0

\frac{d}{d x} (x ln (x^{2} + x))

\int \frac{e ^{2 t}}{2} d t

x \to \frac{π}{2} + lim (cos (x))

What is the derivative of (-u^2+8)/((u^2+8)^2) ?
The derivative of (-u^2+8)/((u^2+8)^2) is -(2u(-u^2+24))/((u^2+8)^3)
What is the first derivative of (-u^2+8)/((u^2+8)^2) ?
The first derivative of (-u^2+8)/((u^2+8)^2) is -(2u(-u^2+24))/((u^2+8)^3)