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

The derivative of (x^2+2x-2/(x^2-2x+2)) is (-4x^2+8x)/((x^2-2x+2)^2)

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

The first derivative of (x^2+2x-2/(x^2-2x+2)) is (-4x^2+8x)/((x^2-2x+2)^2)

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

\frac{- 4 x ^{2} + 8 x}{( x ^{2} - 2 x + 2 ) ^{2}}

Solution steps

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

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

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

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

Expand

(2 x + 2) (x^{2} - 2 x + 2) - (2 x - 2) (x^{2} + 2 x - 2) : - 4 x^{2} + 8 x

= \frac{- 4 x ^{2} + 8 x}{( x ^{2} - 2 x + 2 ) ^{2}}

\int \frac{1}{x ^{2} 324 - x ^{2}} d x

\int cos (9 x) cos (3 x) d x

\int 7 x sec (x) tan (x) d x

\int \frac{1}{( 576 + x ^{2} ) ^{\frac{3}{2}}} d x

\int 2 a cos (\frac{θ}{2}) d θ

What is the derivative of (x^2+2x-2/(x^2-2x+2)) ?
The derivative of (x^2+2x-2/(x^2-2x+2)) is (-4x^2+8x)/((x^2-2x+2)^2)
What is the first derivative of (x^2+2x-2/(x^2-2x+2)) ?
The first derivative of (x^2+2x-2/(x^2-2x+2)) is (-4x^2+8x)/((x^2-2x+2)^2)