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

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

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

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

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

\frac{- x ^{2} - 6}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((x + 2) (x - 3)) = 2 x - 1

= \frac{1 \cdot ( x + 2 ) ( x - 3 ) - ( 2 x - 1 ) x}{( ( x + 2 ) ( x - 3 ) ) ^{2}}

Simplify

\frac{1 \cdot ( x + 2 ) ( x - 3 ) - ( 2 x - 1 ) x}{( ( x + 2 ) ( x - 3 ) ) ^{2}} : \frac{- x ^{2} - 6}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

= \frac{- x ^{2} - 6}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}

arcsin (sin (5 x))

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

\frac{\partial}{\partial y} (y + e^{x})

x \to 3 lim (5 - 2 x + x^{2})

\frac{1}{( s ^{2} + 8 s + 15 )}

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