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

The derivative of (x-4/(-x^2+4)) is (x^2-8x+4)/((-x^2+4)^2)

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

The first derivative of (x-4/(-x^2+4)) is (x^2-8x+4)/((-x^2+4)^2)

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

\frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 4) = 1

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

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

Simplify

\frac{1 \cdot ( - x ^{2} + 4 ) - ( - 2 x ) ( x - 4 )}{( - x ^{2} + 4 ) ^{2}} : \frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 4}{( - x ^{2} + 4 ) ^{2}}

\frac{( 2 s + 1 )}{s ^{2} + 2 s + 5}

\int (x^{2} ln (x)) d x

\frac{\partial}{\partial x} (cos^{2} (3 x))

\frac{d y}{d x} + 2 y = x y^{- 2}

ln (144 sin^{2} (x))

What is the derivative of (x-4/(-x^2+4)) ?
The derivative of (x-4/(-x^2+4)) is (x^2-8x+4)/((-x^2+4)^2)
What is the first derivative of (x-4/(-x^2+4)) ?
The first derivative of (x-4/(-x^2+4)) is (x^2-8x+4)/((-x^2+4)^2)