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Popular >

derivative of u/(u^2+7)

Solution

derivative of

\frac{u}{u ^{2} + 7}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot ( u ^{2} + 7 ) - 2 uu}{( u ^{2} + 7 ) ^{2}}

1 \cdot (u^{2} + 7) - 2 uu = - u^{2} + 7

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

Popular Examples

integral of t^{-1}

\int t^{- 1} d t

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\int (4 x - \frac{4}{x}) d x

derivative of x^3(x-8)^2 derivative of

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tangent of y=(36)/(x^2+2),(1,12)tangent of

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(\partial)/(\partial x)((ax-5)/(-y^2+1))

\frac{\partial}{\partial x} (\frac{a x - 5}{- y ^{2} + 1})

Frequently Asked Questions (FAQ)

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