What is the derivative of (7x-1)/(x^2+9x) ?

The derivative of (7x-1)/(x^2+9x) is (-7x^2+2x+9)/((x^2+9x)^2)

What is the first derivative of (7x-1)/(x^2+9x) ?

The first derivative of (7x-1)/(x^2+9x) is (-7x^2+2x+9)/((x^2+9x)^2)

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derivative of

\frac{7 x - 1}{x ^{2} + 9 x}

\frac{- 7 x ^{2} + 2 x + 9}{( x ^{2} + 9 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x - 1}{x ^{2} + 9 x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 7 x - 1 ) ( x ^{2} + 9 x ) - \frac{d}{d x} ( x ^{2} + 9 x ) ( 7 x - 1 )}{( x ^{2} + 9 x ) ^{2}}

\frac{d}{d x} (7 x - 1) = 7

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

= \frac{7 ( x ^{2} + 9 x ) - ( 2 x + 9 ) ( 7 x - 1 )}{( x ^{2} + 9 x ) ^{2}}

Expand

7 (x^{2} + 9 x) - (2 x + 9) (7 x - 1) : - 7 x^{2} + 2 x + 9

= \frac{- 7 x ^{2} + 2 x + 9}{( x ^{2} + 9 x ) ^{2}}

\int_{- 11}^{0} x 25 - x d x

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

\frac{\partial}{\partial x} (4 sin (x))

\int_{- 2}^{1} (x + 1) x + 3 d x

x^{3} + 2 x - 1

What is the derivative of (7x-1)/(x^2+9x) ?
The derivative of (7x-1)/(x^2+9x) is (-7x^2+2x+9)/((x^2+9x)^2)
What is the first derivative of (7x-1)/(x^2+9x) ?
The first derivative of (7x-1)/(x^2+9x) is (-7x^2+2x+9)/((x^2+9x)^2)