What is the derivative of (3-x^2)/(8+x^2) ?

The derivative of (3-x^2)/(8+x^2) is -(22x)/((8+x^2)^2)

What is the first derivative of (3-x^2)/(8+x^2) ?

The first derivative of (3-x^2)/(8+x^2) is -(22x)/((8+x^2)^2)

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derivative of

\frac{3 - x ^{2}}{8 + x ^{2}}

- \frac{22 x}{( 8 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 - x ^{2}}{8 + x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 - x ^{2} ) ( 8 + x ^{2} ) - \frac{d}{d x} ( 8 + x ^{2} ) ( 3 - x ^{2} )}{( 8 + x ^{2} ) ^{2}}

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

\frac{d}{d x} (8 + x^{2}) = 2 x

= \frac{( - 2 x ) ( 8 + x ^{2} ) - 2 x ( 3 - x ^{2} )}{( 8 + x ^{2} ) ^{2}}

Simplify

\frac{( - 2 x ) ( 8 + x ^{2} ) - 2 x ( 3 - x ^{2} )}{( 8 + x ^{2} ) ^{2}} : - \frac{22 x}{( 8 + x ^{2} ) ^{2}}

= - \frac{22 x}{( 8 + x ^{2} ) ^{2}}

x \to 0 lim (sin (2 x) csc (3 x))

\frac{d p}{d x}, x^{2} + 3 p x + p^{2} = 79

\frac{d}{d x} (- \frac{9}{( x + 1 ) ^{2}} + 1)

\int p (p + 9)^{6} d p

f (x) = \frac{1}{3} (5 - x)^{4}

What is the derivative of (3-x^2)/(8+x^2) ?
The derivative of (3-x^2)/(8+x^2) is -(22x)/((8+x^2)^2)
What is the first derivative of (3-x^2)/(8+x^2) ?
The first derivative of (3-x^2)/(8+x^2) is -(22x)/((8+x^2)^2)