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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

2 x (x^{2} + 2) - 2 x (x^{2} - 2) : 8 x

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

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