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

The derivative of (2x+5/(x^2+5x)) is (-2x^2-10x-25)/((x^2+5x)^2)

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

The first derivative of (2x+5/(x^2+5x)) is (-2x^2-10x-25)/((x^2+5x)^2)

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

\frac{- 2 x ^{2} - 10 x - 25}{( x ^{2} + 5 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( x ^{2} + 5 x ) - ( 2 x + 5 ) ( 2 x + 5 )}{( x ^{2} + 5 x ) ^{2}} : \frac{- 2 x ^{2} - 10 x - 25}{( x ^{2} + 5 x ) ^{2}}

= \frac{- 2 x ^{2} - 10 x - 25}{( x ^{2} + 5 x ) ^{2}}

\int \frac{11}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

\frac{d}{d x} (\frac{x ^{(2)}}{sin ( x )})

f (x) = 3^{x}, at x = 1

\int_{1}^{e} \frac{2 x - 3 x ^{3}}{x ^{2}} d x

f (x) = x^{2} + 4 x

What is the derivative of (2x+5/(x^2+5x)) ?
The derivative of (2x+5/(x^2+5x)) is (-2x^2-10x-25)/((x^2+5x)^2)
What is the first derivative of (2x+5/(x^2+5x)) ?
The first derivative of (2x+5/(x^2+5x)) is (-2x^2-10x-25)/((x^2+5x)^2)