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

The derivative of (5-x^2)/((5+x^2)^2) is -(2x(-x^2+15))/((x^2+5)^3)

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

The first derivative of (5-x^2)/((5+x^2)^2) is -(2x(-x^2+15))/((x^2+5)^3)

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derivative of

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

- \frac{2 x ( - x ^{2} + 15 )}{( x ^{2} + 5 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - 2 x ) ( 5 + x ^{2} ) ^{2} - 4 x ( 5 + x ^{2} ) ( 5 - x ^{2} )}{( ( 5 + x ^{2} ) ^{2} ) ^{2}} : - \frac{2 x ( - x ^{2} + 15 )}{( x ^{2} + 5 ) ^{3}}

= - \frac{2 x ( - x ^{2} + 15 )}{( x ^{2} + 5 ) ^{3}}

\frac{d}{d x} (3 x^{\frac{3}{2}} - 1)

\int \frac{36}{x ^{3}} d x

x \to 1 lim (9)

\int sin (5 x) cos (7 x) d x

\frac{5}{x}, \frac{5}{x ^{2}}, 1, 4

What is the derivative of (5-x^2)/((5+x^2)^2) ?
The derivative of (5-x^2)/((5+x^2)^2) is -(2x(-x^2+15))/((x^2+5)^3)
What is the first derivative of (5-x^2)/((5+x^2)^2) ?
The first derivative of (5-x^2)/((5+x^2)^2) is -(2x(-x^2+15))/((x^2+5)^3)