What is the derivative of (x^2-2/(-x^2+1)) ?

The derivative of (x^2-2/(-x^2+1)) is -(2x)/((-x^2+1)^2)

What is the first derivative of (x^2-2/(-x^2+1)) ?

The first derivative of (x^2-2/(-x^2+1)) is -(2x)/((-x^2+1)^2)

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (arcsin (2 x - 1))

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

\frac{d}{d x} (30 e^{x})

\frac{d}{d x} (22 x)

\frac{d}{d x} (\frac{x}{e ^{- x}})

What is the derivative of (x^2-2/(-x^2+1)) ?
The derivative of (x^2-2/(-x^2+1)) is -(2x)/((-x^2+1)^2)
What is the first derivative of (x^2-2/(-x^2+1)) ?
The first derivative of (x^2-2/(-x^2+1)) is -(2x)/((-x^2+1)^2)