What is the derivative of (x^2-2x+5/(x^2+9)) ?

The derivative of (x^2-2x+5/(x^2+9)) is (2x^2+8x-18)/((x^2+9)^2)

What is the first derivative of (x^2-2x+5/(x^2+9)) ?

The first derivative of (x^2-2x+5/(x^2+9)) is (2x^2+8x-18)/((x^2+9)^2)

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\frac{d}{d x} (\frac{x ^{2} - 2 x + 5}{x ^{2} + 9})

\frac{2 x ^{2} + 8 x - 18}{( x ^{2} + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 2 x + 5}{x ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 2 x + 5 ) ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) ( x ^{2} - 2 x + 5 )}{( x ^{2} + 9 ) ^{2}}

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

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

= \frac{( 2 x - 2 ) ( x ^{2} + 9 ) - 2 x ( x ^{2} - 2 x + 5 )}{( x ^{2} + 9 ) ^{2}}

Expand

(2 x - 2) (x^{2} + 9) - 2 x (x^{2} - 2 x + 5) : 2 x^{2} + 8 x - 18

= \frac{2 x ^{2} + 8 x - 18}{( x ^{2} + 9 ) ^{2}}

\int (- \frac{3}{10 - 10 x ^{2}}) d x

y = 3 tan (2 x)

\int \frac{- 6}{x ^{2} x ^{2} - 9} d x

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

\frac{5}{s ^{2} + 12}

What is the derivative of (x^2-2x+5/(x^2+9)) ?
The derivative of (x^2-2x+5/(x^2+9)) is (2x^2+8x-18)/((x^2+9)^2)
What is the first derivative of (x^2-2x+5/(x^2+9)) ?
The first derivative of (x^2-2x+5/(x^2+9)) is (2x^2+8x-18)/((x^2+9)^2)