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

The derivative of (3-3x-x^2/(x^2-5)) is (3x^2+4x+15)/((x^2-5)^2)

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

The first derivative of (3-3x-x^2/(x^2-5)) is (3x^2+4x+15)/((x^2-5)^2)

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

\frac{3 x ^{2} + 4 x + 15}{( x ^{2} - 5 ) ^{2}}

Solution steps

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

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

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

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

Expand

(- 2 x - 3) (x^{2} - 5) - 2 x (3 - 3 x - x^{2}) : 3 x^{2} + 4 x + 15

= \frac{3 x ^{2} + 4 x + 15}{( x ^{2} - 5 ) ^{2}}

\int \frac{1}{3 - x} d x

\int_{1}^{l n (x)} \frac{1}{x} d x

\frac{d}{d x} (3 π^{4})

\int 10 - 4 x - 4 x^{2} d x

\frac{\partial}{\partial z} (2 e^{x} cos (yz))

What is the derivative of (3-3x-x^2/(x^2-5)) ?
The derivative of (3-3x-x^2/(x^2-5)) is (3x^2+4x+15)/((x^2-5)^2)
What is the first derivative of (3-3x-x^2/(x^2-5)) ?
The first derivative of (3-3x-x^2/(x^2-5)) is (3x^2+4x+15)/((x^2-5)^2)