What is the derivative of (x+2/(x^2+4x+13)) ?

The derivative of (x+2/(x^2+4x+13)) is (-x^2-4x+5)/((x^2+4x+13)^2)

What is the first derivative of (x+2/(x^2+4x+13)) ?

The first derivative of (x+2/(x^2+4x+13)) is (-x^2-4x+5)/((x^2+4x+13)^2)

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\frac{d}{d x} (\frac{x + 2}{x ^{2} + 4 x + 13})

\frac{- x ^{2} - 4 x + 5}{( x ^{2} + 4 x + 13 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 2}{x ^{2} + 4 x + 13})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 2 ) ( x ^{2} + 4 x + 13 ) - \frac{d}{d x} ( x ^{2} + 4 x + 13 ) ( x + 2 )}{( x ^{2} + 4 x + 13 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 4 x + 13) = 2 x + 4

= \frac{1 \cdot ( x ^{2} + 4 x + 13 ) - ( 2 x + 4 ) ( x + 2 )}{( x ^{2} + 4 x + 13 ) ^{2}}

Simplify

\frac{1 \cdot ( x ^{2} + 4 x + 13 ) - ( 2 x + 4 ) ( x + 2 )}{( x ^{2} + 4 x + 13 ) ^{2}} : \frac{- x ^{2} - 4 x + 5}{( x ^{2} + 4 x + 13 ) ^{2}}

= \frac{- x ^{2} - 4 x + 5}{( x ^{2} + 4 x + 13 ) ^{2}}

\frac{\partial}{\partial y} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

d er i v a t i v e f (x) = sin^{2} (tan (x))

\frac{d}{d t} (- \frac{1}{t + 1})

d er i v a t i v e f (x) = \frac{x}{a}

t an g e n t f (x) = x^{2} (4 - x)^{2}, at x = 1

What is the derivative of (x+2/(x^2+4x+13)) ?
The derivative of (x+2/(x^2+4x+13)) is (-x^2-4x+5)/((x^2+4x+13)^2)
What is the first derivative of (x+2/(x^2+4x+13)) ?
The first derivative of (x+2/(x^2+4x+13)) is (-x^2-4x+5)/((x^2+4x+13)^2)