What is the derivative of x/(x^2+13x+40) ?

The derivative of x/(x^2+13x+40) is (-x^2+40)/((x^2+13x+40)^2)

What is the first derivative of x/(x^2+13x+40) ?

The first derivative of x/(x^2+13x+40) is (-x^2+40)/((x^2+13x+40)^2)

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derivative of

\frac{x}{x ^{2} + 13 x + 40}

\frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x ^{2} + 13 x + 40})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 13 x + 40 ) - \frac{d}{d x} ( x ^{2} + 13 x + 40 ) x}{( x ^{2} + 13 x + 40 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 13 x + 40) = 2 x + 13

= \frac{1 \cdot ( x ^{2} + 13 x + 40 ) - ( 2 x + 13 ) x}{( x ^{2} + 13 x + 40 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} + 13 x + 40 ) - ( 2 x + 13 ) x}{( x ^{2} + 13 x + 40 ) ^{2}} : \frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

= \frac{- x ^{2} + 40}{( x ^{2} + 13 x + 40 ) ^{2}}

What is the derivative of x/(x^2+13x+40) ?
The derivative of x/(x^2+13x+40) is (-x^2+40)/((x^2+13x+40)^2)
What is the first derivative of x/(x^2+13x+40) ?
The first derivative of x/(x^2+13x+40) is (-x^2+40)/((x^2+13x+40)^2)