What is the derivative of (2x+3/(x^2-9)) ?

The derivative of (2x+3/(x^2-9)) is (-2x^2-6x-18)/((x^2-9)^2)

What is the first derivative of (2x+3/(x^2-9)) ?

The first derivative of (2x+3/(x^2-9)) is (-2x^2-6x-18)/((x^2-9)^2)

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\frac{d}{d x} (\frac{2 x + 3}{x ^{2} - 9})

\frac{- 2 x ^{2} - 6 x - 18}{( x ^{2} - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 3}{x ^{2} - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 3 ) ( x ^{2} - 9 ) - \frac{d}{d x} ( x ^{2} - 9 ) ( 2 x + 3 )}{( x ^{2} - 9 ) ^{2}}

\frac{d}{d x} (2 x + 3) = 2

\frac{d}{d x} (x^{2} - 9) = 2 x

= \frac{2 ( x ^{2} - 9 ) - 2 x ( 2 x + 3 )}{( x ^{2} - 9 ) ^{2}}

Expand

2 (x^{2} - 9) - 2 x (2 x + 3) : - 2 x^{2} - 6 x - 18

= \frac{- 2 x ^{2} - 6 x - 18}{( x ^{2} - 9 ) ^{2}}

y = x^{4} + 9 e^{x}, (0, 5)

\int h^{- \frac{1}{2}} d h

\frac{\partial}{\partial y} (x^{2} + cos (y))

x \to 81 lim (\frac{( x - 9 )}{x - 81})

\int cos^{2} (x + \frac{π}{2}) d x

What is the derivative of (2x+3/(x^2-9)) ?
The derivative of (2x+3/(x^2-9)) is (-2x^2-6x-18)/((x^2-9)^2)
What is the first derivative of (2x+3/(x^2-9)) ?
The first derivative of (2x+3/(x^2-9)) is (-2x^2-6x-18)/((x^2-9)^2)