What is the derivative of (-u^2+7)/((u^2+7)^2) ?

The derivative of (-u^2+7)/((u^2+7)^2) is -(2u(-u^2+21))/((u^2+7)^3)

What is the first derivative of (-u^2+7)/((u^2+7)^2) ?

The first derivative of (-u^2+7)/((u^2+7)^2) is -(2u(-u^2+21))/((u^2+7)^3)

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derivative of

\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}

- \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

Solution steps

\frac{d}{d u} (\frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d u} ( - u ^{2} + 7 ) ( u ^{2} + 7 ) ^{2} - \frac{d}{d u} ( ( u ^{2} + 7 ) ^{2} ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}}

\frac{d}{d u} (- u^{2} + 7) = - 2 u

\frac{d}{d u} ((u^{2} + 7)^{2}) = 4 u (u^{2} + 7)

= \frac{( - 2 u ) ( u ^{2} + 7 ) ^{2} - 4 u ( u ^{2} + 7 ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}}

Simplify

\frac{( - 2 u ) ( u ^{2} + 7 ) ^{2} - 4 u ( u ^{2} + 7 ) ( - u ^{2} + 7 )}{( ( u ^{2} + 7 ) ^{2} ) ^{2}} : - \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

= - \frac{2 u ( - u ^{2} + 21 )}{( u ^{2} + 7 ) ^{3}}

\frac{d}{d x} (sec (x^{5} + x))

(1.1) (0.5)

\int 1 + 5 x^{2} (10 x) d x

y = 3 x^{2} + \frac{10 x}{3} - 2

\frac{d}{d x} (\frac{tan ^{3} ( x )}{3})

What is the derivative of (-u^2+7)/((u^2+7)^2) ?
The derivative of (-u^2+7)/((u^2+7)^2) is -(2u(-u^2+21))/((u^2+7)^3)
What is the first derivative of (-u^2+7)/((u^2+7)^2) ?
The first derivative of (-u^2+7)/((u^2+7)^2) is -(2u(-u^2+21))/((u^2+7)^3)