What is the derivative of f(x)=(5x-7)/(6x-9) ?

The derivative of f(x)=(5x-7)/(6x-9) is -1/(3(2x-3)^2)

What is the first derivative of f(x)=(5x-7)/(6x-9) ?

The first derivative of f(x)=(5x-7)/(6x-9) is -1/(3(2x-3)^2)

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derivative of

f (x) = \frac{5 x - 7}{6 x - 9}

- \frac{1}{3 ( 2 x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x - 7}{6 x - 9})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x - 7 ) ( 6 x - 9 ) - \frac{d}{d x} ( 6 x - 9 ) ( 5 x - 7 )}{( 6 x - 9 ) ^{2}}

\frac{d}{d x} (5 x - 7) = 5

\frac{d}{d x} (6 x - 9) = 6

= \frac{5 ( 6 x - 9 ) - 6 ( 5 x - 7 )}{( 6 x - 9 ) ^{2}}

Simplify

\frac{5 ( 6 x - 9 ) - 6 ( 5 x - 7 )}{( 6 x - 9 ) ^{2}} : - \frac{1}{3 ( 2 x - 3 ) ^{2}}

= - \frac{1}{3 ( 2 x - 3 ) ^{2}}

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\frac{d y}{d t} = 7 t e^{- y}, y (0) = 3

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What is the derivative of f(x)=(5x-7)/(6x-9) ?
The derivative of f(x)=(5x-7)/(6x-9) is -1/(3(2x-3)^2)
What is the first derivative of f(x)=(5x-7)/(6x-9) ?
The first derivative of f(x)=(5x-7)/(6x-9) is -1/(3(2x-3)^2)