What is the derivative of f(x)=(2x-3)/(x^2+2x) ?

The derivative of f(x)=(2x-3)/(x^2+2x) is (-2x^2+6x+6)/((x^2+2x)^2)

What is the first derivative of f(x)=(2x-3)/(x^2+2x) ?

The first derivative of f(x)=(2x-3)/(x^2+2x) is (-2x^2+6x+6)/((x^2+2x)^2)

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derivative of

f (x) = \frac{2 x - 3}{x ^{2} + 2 x}

\frac{- 2 x ^{2} + 6 x + 6}{( x ^{2} + 2 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 3}{x ^{2} + 2 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x - 3 ) ( x ^{2} + 2 x ) - \frac{d}{d x} ( x ^{2} + 2 x ) ( 2 x - 3 )}{( x ^{2} + 2 x ) ^{2}}

\frac{d}{d x} (2 x - 3) = 2

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

= \frac{2 ( x ^{2} + 2 x ) - ( 2 x + 2 ) ( 2 x - 3 )}{( x ^{2} + 2 x ) ^{2}}

Expand

2 (x^{2} + 2 x) - (2 x + 2) (2 x - 3) : - 2 x^{2} + 6 x + 6

= \frac{- 2 x ^{2} + 6 x + 6}{( x ^{2} + 2 x ) ^{2}}

2 x^{3} - e^{x y} = x \cdot y^{4}

x \to 0 + lim (x^{9 x})

\frac{\partial}{\partial x} (5 x^{2})

\int \frac{x}{6 - x ^{2}} d x

x \to 3 lim (x^{2})

What is the derivative of f(x)=(2x-3)/(x^2+2x) ?
The derivative of f(x)=(2x-3)/(x^2+2x) is (-2x^2+6x+6)/((x^2+2x)^2)
What is the first derivative of f(x)=(2x-3)/(x^2+2x) ?
The first derivative of f(x)=(2x-3)/(x^2+2x) is (-2x^2+6x+6)/((x^2+2x)^2)