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Popular >

derivative of u/(u^2+8)

Solution

derivative of

\frac{u}{u ^{2} + 8}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d u}{d u} = 1

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

= \frac{1 \cdot ( u ^{2} + 8 ) - 2 uu}{( u ^{2} + 8 ) ^{2}}

1 \cdot (u^{2} + 8) - 2 uu = - u^{2} + 8

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

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Frequently Asked Questions (FAQ)

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