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Popular >

derivative of u/(u^2+5)

Solution

derivative of

\frac{u}{u ^{2} + 5}

Solution

\frac{- u ^{2} + 5}{( u ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d u} (\frac{u}{u ^{2} + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d u}{d u} ( u ^{2} + 5 ) - \frac{d}{d u} ( u ^{2} + 5 ) u}{( u ^{2} + 5 ) ^{2}}

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

\frac{d}{d u} (u^{2} + 5) = 2 u

= \frac{1 \cdot ( u ^{2} + 5 ) - 2 uu}{( u ^{2} + 5 ) ^{2}}

1 \cdot (u^{2} + 5) - 2 uu = - u^{2} + 5

= \frac{- u ^{2} + 5}{( u ^{2} + 5 ) ^{2}}

Popular Examples

integral of e^{(-0.1x)}

\int e^{(- 0.1 x)} d x

derivative of x^2-x+5

\frac{d}{d x} (x^{2} - x + 5)

integral from-1 to 1 of x^3-3x^2-x+3

\int_{- 1}^{1} x^{3} - 3 x^{2} - x + 3 d x

integral of (5x^2+7x+5)/((x^2+1)^2)

\int \frac{5 x ^{2} + 7 x + 5}{( x ^{2} + 1 ) ^{2}} d x

derivative of (x+5(x-1)(x-7))

\frac{d}{d x} ((x + 5) (x - 1) (x - 7))

Frequently Asked Questions (FAQ)

What is the derivative of u/(u^2+5) ?
The derivative of u/(u^2+5) is (-u^2+5)/((u^2+5)^2)
What is the first derivative of u/(u^2+5) ?
The first derivative of u/(u^2+5) is (-u^2+5)/((u^2+5)^2)