What is the derivative of (x^2+4/(x^2-4)) ?

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{30 x ^{5}}{2 + 5 x ^{6}} d x

\int \frac{x ^{2} - x + 4}{x ^{3} + 2 x} d x

2 sin (3 t) + cos (2 t) + 3 e^{- 2 t} cos (t)

\int \frac{( x - 1 )}{x ^{5}} d x

\frac{\partial}{\partial z} (sin (z))

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