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

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

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

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

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derivative of

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

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

Solution steps

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

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

Expand

2 x (x^{2} + x - 2) - (2 x + 1) x^{2} : x^{2} - 4 x

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

\int (x^{2} - 3) sin (2 x) d x

\frac{d}{d x} (sin (x) + sin (y) + sin (x + y))

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

\frac{d}{d x} (\frac{cos ( x ) - 1}{sin ( x )})

(2 e^{- t}) (cos (4 t)) (1 (t))

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