What is the derivative of (x^2/((x^2+5)^3)) ?

The derivative of (x^2/((x^2+5)^3)) is (2x(-2x^2+5))/((x^2+5)^4)

What is the first derivative of (x^2/((x^2+5)^3)) ?

The first derivative of (x^2/((x^2+5)^3)) is (2x(-2x^2+5))/((x^2+5)^4)

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\frac{d}{d x} (\frac{x ^{2}}{( x ^{2} + 5 ) ^{3}})

\frac{2 x ( - 2 x ^{2} + 5 )}{( x ^{2} + 5 ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{( x ^{2} + 5 ) ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} + 5 ) ^{3} - \frac{d}{d x} ( ( x ^{2} + 5 ) ^{3} ) x ^{2}}{( ( x ^{2} + 5 ) ^{3} ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x^{2} + 5)^{3}) = 6 x (x^{2} + 5)^{2}

= \frac{2 x ( x ^{2} + 5 ) ^{3} - 6 x ( x ^{2} + 5 ) ^{2} x ^{2}}{( ( x ^{2} + 5 ) ^{3} ) ^{2}}

Simplify

\frac{2 x ( x ^{2} + 5 ) ^{3} - 6 x ( x ^{2} + 5 ) ^{2} x ^{2}}{( ( x ^{2} + 5 ) ^{3} ) ^{2}} : \frac{2 x ( - 2 x ^{2} + 5 )}{( x ^{2} + 5 ) ^{4}}

= \frac{2 x ( - 2 x ^{2} + 5 )}{( x ^{2} + 5 ) ^{4}}

9 y^{7} + 4 x^{3} = 8 y + 5 x, (1, 1)

\frac{\partial}{\partial x} (cos^{5} (x^{7} y^{5}))

x y^{^{'}} + (1 - x) y = 0

\frac{d N}{d t} = N (1 - 0.0005 N)

x \frac{d y}{d x} + y = (x y)^{\frac{3}{2}}

What is the derivative of (x^2/((x^2+5)^3)) ?
The derivative of (x^2/((x^2+5)^3)) is (2x(-2x^2+5))/((x^2+5)^4)
What is the first derivative of (x^2/((x^2+5)^3)) ?
The first derivative of (x^2/((x^2+5)^3)) is (2x(-2x^2+5))/((x^2+5)^4)