What is the derivative of (x^2-9x+1)/(x^2+5) ?

The derivative of (x^2-9x+1)/(x^2+5) is (9x^2+8x-45)/((x^2+5)^2)

What is the first derivative of (x^2-9x+1)/(x^2+5) ?

The first derivative of (x^2-9x+1)/(x^2+5) is (9x^2+8x-45)/((x^2+5)^2)

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derivative of

\frac{x ^{2} - 9 x + 1}{x ^{2} + 5}

\frac{9 x ^{2} + 8 x - 45}{( x ^{2} + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} - 9 x + 1}{x ^{2} + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} - 9 x + 1 ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) ( x ^{2} - 9 x + 1 )}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (x^{2} - 9 x + 1) = 2 x - 9

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

= \frac{( 2 x - 9 ) ( x ^{2} + 5 ) - 2 x ( x ^{2} - 9 x + 1 )}{( x ^{2} + 5 ) ^{2}}

Expand

(2 x - 9) (x^{2} + 5) - 2 x (x^{2} - 9 x + 1) : 9 x^{2} + 8 x - 45

= \frac{9 x ^{2} + 8 x - 45}{( x ^{2} + 5 ) ^{2}}

What is the derivative of (x^2-9x+1)/(x^2+5) ?
The derivative of (x^2-9x+1)/(x^2+5) is (9x^2+8x-45)/((x^2+5)^2)
What is the first derivative of (x^2-9x+1)/(x^2+5) ?
The first derivative of (x^2-9x+1)/(x^2+5) is (9x^2+8x-45)/((x^2+5)^2)