What is the derivative of (2-5x-x^2/(x^2-6)) ?

The derivative of (2-5x-x^2/(x^2-6)) is (5x^2+8x+30)/((x^2-6)^2)

What is the first derivative of (2-5x-x^2/(x^2-6)) ?

The first derivative of (2-5x-x^2/(x^2-6)) is (5x^2+8x+30)/((x^2-6)^2)

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\frac{d}{d x} (\frac{2 - 5 x - x ^{2}}{x ^{2} - 6})

\frac{5 x ^{2} + 8 x + 30}{( x ^{2} - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 - 5 x - x ^{2}}{x ^{2} - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 - 5 x - x ^{2} ) ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) ( 2 - 5 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 6) = 2 x

= \frac{( - 2 x - 5 ) ( x ^{2} - 6 ) - 2 x ( 2 - 5 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

Expand

(- 2 x - 5) (x^{2} - 6) - 2 x (2 - 5 x - x^{2}) : 5 x^{2} + 8 x + 30

= \frac{5 x ^{2} + 8 x + 30}{( x ^{2} - 6 ) ^{2}}

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

\frac{d y}{d x} = 2 x \cdot e^{- y}

\int \frac{x}{x - 10} d x

n = 1 \sum \infty n 2

y^{^{'}} - 2 = 2 y^{2}

What is the derivative of (2-5x-x^2/(x^2-6)) ?
The derivative of (2-5x-x^2/(x^2-6)) is (5x^2+8x+30)/((x^2-6)^2)
What is the first derivative of (2-5x-x^2/(x^2-6)) ?
The first derivative of (2-5x-x^2/(x^2-6)) is (5x^2+8x+30)/((x^2-6)^2)