What is the derivative of (2(16-x^2)/((16+x^2)^2)) ?

The derivative of (2(16-x^2)/((16+x^2)^2)) is -(4x(-x^2+48))/((x^2+16)^3)

What is the first derivative of (2(16-x^2)/((16+x^2)^2)) ?

The first derivative of (2(16-x^2)/((16+x^2)^2)) is -(4x(-x^2+48))/((x^2+16)^3)

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\frac{d}{d x} (\frac{2 ( 16 - x ^{2} )}{( 16 + x ^{2} ) ^{2}})

- \frac{4 x ( - x ^{2} + 48 )}{( x ^{2} + 16 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 ( 16 - x ^{2} )}{( 16 + x ^{2} ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{16 - x ^{2}}{( 16 + x ^{2} ) ^{2}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d}{d x} ( 16 - x ^{2} ) ( 16 + x ^{2} ) ^{2} - \frac{d}{d x} ( ( 16 + x ^{2} ) ^{2} ) ( 16 - x ^{2} )}{( ( 16 + x ^{2} ) ^{2} ) ^{2}}

\frac{d}{d x} (16 - x^{2}) = - 2 x

\frac{d}{d x} ((16 + x^{2})^{2}) = 4 x (16 + x^{2})

= 2 \cdot \frac{( - 2 x ) ( 16 + x ^{2} ) ^{2} - 4 x ( 16 + x ^{2} ) ( 16 - x ^{2} )}{( ( 16 + x ^{2} ) ^{2} ) ^{2}}

Simplify

2 \cdot \frac{( - 2 x ) ( 16 + x ^{2} ) ^{2} - 4 x ( 16 + x ^{2} ) ( 16 - x ^{2} )}{( ( 16 + x ^{2} ) ^{2} ) ^{2}} : - \frac{4 x ( - x ^{2} + 48 )}{( x ^{2} + 16 ) ^{3}}

= - \frac{4 x ( - x ^{2} + 48 )}{( x ^{2} + 16 ) ^{3}}

\int (cos (x) + sin (x)) d x

\frac{d}{d x} (a sin (5 x))

x \to - 3 lim (\frac{x ^{2}}{x ^{2} - 9})

\frac{\partial}{\partial x} (x sin (x^{2} - y^{2}))

(x + y e^{\frac{y}{x}}) d x - (x e^{\frac{y}{x}}) d y = 0

What is the derivative of (2(16-x^2)/((16+x^2)^2)) ?
The derivative of (2(16-x^2)/((16+x^2)^2)) is -(4x(-x^2+48))/((x^2+16)^3)
What is the first derivative of (2(16-x^2)/((16+x^2)^2)) ?
The first derivative of (2(16-x^2)/((16+x^2)^2)) is -(4x(-x^2+48))/((x^2+16)^3)