What is the derivative of (2x/((x+2)(x-5)^2)) ?

The derivative of (2x/((x+2)(x-5)^2)) is -(4(x^2+x+5))/((x+2)^2(x-5)^3)

What is the first derivative of (2x/((x+2)(x-5)^2)) ?

The first derivative of (2x/((x+2)(x-5)^2)) is -(4(x^2+x+5))/((x+2)^2(x-5)^3)

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\frac{d}{d x} (\frac{2 x}{( x + 2 ) ( x - 5 ) ^{2}})

- \frac{4 ( x ^{2} + x + 5 )}{( x + 2 ) ^{2} ( x - 5 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x}{( x + 2 ) ( x - 5 ) ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (\frac{x}{( x + 2 ) ( x - 5 ) ^{2}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( x + 2 ) ( x - 5 ) ^{2} - \frac{d}{d x} ( ( x + 2 ) ( x - 5 ) ^{2} ) x}{( ( x + 2 ) ( x - 5 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x + 2) (x - 5)^{2}) = 3 x^{2} - 16 x + 5

= 2 \cdot \frac{1 \cdot ( x + 2 ) ( x - 5 ) ^{2} - ( 3 x ^{2} - 16 x + 5 ) x}{( ( x + 2 ) ( x - 5 ) ^{2} ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x + 2 ) ( x - 5 ) ^{2} - ( 3 x ^{2} - 16 x + 5 ) x}{( ( x + 2 ) ( x - 5 ) ^{2} ) ^{2}} : - \frac{4 ( x ^{2} + x + 5 )}{( x + 2 ) ^{2} ( x - 5 ) ^{3}}

= - \frac{4 ( x ^{2} + x + 5 )}{( x + 2 ) ^{2} ( x - 5 ) ^{3}}

\int_{1}^{2} ln (x) d x

\frac{d}{d x} (2 x - 8)

\frac{d ^{2}}{d x ^{2}} (9 cos (2 x))

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

x \to 0 lim (\frac{e ^{x^{2}} - 1}{x})

What is the derivative of (2x/((x+2)(x-5)^2)) ?
The derivative of (2x/((x+2)(x-5)^2)) is -(4(x^2+x+5))/((x+2)^2(x-5)^3)
What is the first derivative of (2x/((x+2)(x-5)^2)) ?
The first derivative of (2x/((x+2)(x-5)^2)) is -(4(x^2+x+5))/((x+2)^2(x-5)^3)