What is the derivative of (6x-1)/(2x+9) ?

The derivative of (6x-1)/(2x+9) is (56)/((2x+9)^2)

What is the first derivative of (6x-1)/(2x+9) ?

The first derivative of (6x-1)/(2x+9) is (56)/((2x+9)^2)

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derivative of

\frac{6 x - 1}{2 x + 9}

\frac{56}{( 2 x + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 x - 1}{2 x + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x - 1 ) ( 2 x + 9 ) - \frac{d}{d x} ( 2 x + 9 ) ( 6 x - 1 )}{( 2 x + 9 ) ^{2}}

\frac{d}{d x} (6 x - 1) = 6

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

= \frac{6 ( 2 x + 9 ) - 2 ( 6 x - 1 )}{( 2 x + 9 ) ^{2}}

Expand

6 (2 x + 9) - 2 (6 x - 1) : 56

= \frac{56}{( 2 x + 9 ) ^{2}}

\int e^{- z^{2}} d z

\int \frac{x}{x ^{2} + 4} d x

x \to 2 lim (- \frac{1}{( x - 2 ) ^{2}})

y = x^{2} - x + 7, at x = 7

x \to 1 lim (\frac{x ^{9} - 1}{x - 1})

What is the derivative of (6x-1)/(2x+9) ?
The derivative of (6x-1)/(2x+9) is (56)/((2x+9)^2)
What is the first derivative of (6x-1)/(2x+9) ?
The first derivative of (6x-1)/(2x+9) is (56)/((2x+9)^2)