What is the derivative of (1-4x-x^2/(x^2-5)) ?

The derivative of (1-4x-x^2/(x^2-5)) is (4x^2+8x+20)/((x^2-5)^2)

What is the first derivative of (1-4x-x^2/(x^2-5)) ?

The first derivative of (1-4x-x^2/(x^2-5)) is (4x^2+8x+20)/((x^2-5)^2)

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\frac{d}{d x} (\frac{1 - 4 x - x ^{2}}{x ^{2} - 5})

\frac{4 x ^{2} + 8 x + 20}{( x ^{2} - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 4 x - x ^{2}}{x ^{2} - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - 4 x - x ^{2} ) ( x ^{2} - 5 ) - \frac{d}{d x} ( x ^{2} - 5 ) ( 1 - 4 x - x ^{2} )}{( x ^{2} - 5 ) ^{2}}

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

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

= \frac{( - 2 x - 4 ) ( x ^{2} - 5 ) - 2 x ( 1 - 4 x - x ^{2} )}{( x ^{2} - 5 ) ^{2}}

Expand

(- 2 x - 4) (x^{2} - 5) - 2 x (1 - 4 x - x^{2}) : 4 x^{2} + 8 x + 20

= \frac{4 x ^{2} + 8 x + 20}{( x ^{2} - 5 ) ^{2}}

\int sin^{3} (2 x) cos^{7} (x) d x

\int \frac{1}{x ^{2} - 6 x - 7} d x

x \to 0 lim (\frac{sin ( 5 x )}{x} + 4)

\int (\frac{e ^{x}}{1 + e ^{2 x}}) d x

\int_{2}^{3} \frac{2 t}{1 + t ^{2}} d t

What is the derivative of (1-4x-x^2/(x^2-5)) ?
The derivative of (1-4x-x^2/(x^2-5)) is (4x^2+8x+20)/((x^2-5)^2)
What is the first derivative of (1-4x-x^2/(x^2-5)) ?
The first derivative of (1-4x-x^2/(x^2-5)) is (4x^2+8x+20)/((x^2-5)^2)