What is the derivative of f(x)=(6-x^2)/(6+x^2) ?

The derivative of f(x)=(6-x^2)/(6+x^2) is -(24x)/((6+x^2)^2)

What is the first derivative of f(x)=(6-x^2)/(6+x^2) ?

The first derivative of f(x)=(6-x^2)/(6+x^2) is -(24x)/((6+x^2)^2)

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derivative of

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

- \frac{24 x}{( 6 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 - x ^{2}}{6 + x ^{2}})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (6 - x^{2}) = - 2 x

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

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

Simplify

\frac{( - 2 x ) ( 6 + x ^{2} ) - 2 x ( 6 - x ^{2} )}{( 6 + x ^{2} ) ^{2}} : - \frac{24 x}{( 6 + x ^{2} ) ^{2}}

= - \frac{24 x}{( 6 + x ^{2} ) ^{2}}

\frac{d ^{3}}{d x ^{3}} (ln (1 + x))

k = 1 \sum \infty \frac{k}{e ^{7 k}}

\frac{( e ^{- s} )}{s}

\frac{\partial}{\partial x} (9 x sin (4 x^{2} y))

f (t) = t^{2}

What is the derivative of f(x)=(6-x^2)/(6+x^2) ?
The derivative of f(x)=(6-x^2)/(6+x^2) is -(24x)/((6+x^2)^2)
What is the first derivative of f(x)=(6-x^2)/(6+x^2) ?
The first derivative of f(x)=(6-x^2)/(6+x^2) is -(24x)/((6+x^2)^2)