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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{e ^{4 x^{2}}}{x ^{2}})

x^{2} - 10, 9 x

\int \frac{1}{e ^{2 x} - 4} d x

\int x^{2} ln (4 x) d x

x \to - \frac{π}{4} lim (sec (x))

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