What is the derivative of (3-5x-x^2/(x^2-6)) ?

The derivative of (3-5x-x^2/(x^2-6)) is (5x^2+6x+30)/((x^2-6)^2)

What is the first derivative of (3-5x-x^2/(x^2-6)) ?

The first derivative of (3-5x-x^2/(x^2-6)) is (5x^2+6x+30)/((x^2-6)^2)

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\frac{d}{d x} (\frac{3 - 5 x - x ^{2}}{x ^{2} - 6})

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

Solution steps

\frac{d}{d x} (\frac{3 - 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} ( 3 - 5 x - x ^{2} ) ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) ( 3 - 5 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

\frac{d}{d x} (3 - 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 ( 3 - 5 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

Expand

(- 2 x - 5) (x^{2} - 6) - 2 x (3 - 5 x - x^{2}) : 5 x^{2} + 6 x + 30

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

x \to 0 lim (\frac{x}{x ^{2} - 5 x})

x \to \infty + lim (x^{2})

y = x^{2} - 2 x - 4

cos (x^{3})

\frac{\partial}{\partial z} (x \cdot ln (y - z))

What is the derivative of (3-5x-x^2/(x^2-6)) ?
The derivative of (3-5x-x^2/(x^2-6)) is (5x^2+6x+30)/((x^2-6)^2)
What is the first derivative of (3-5x-x^2/(x^2-6)) ?
The first derivative of (3-5x-x^2/(x^2-6)) is (5x^2+6x+30)/((x^2-6)^2)