What is the derivative of (x-3/(6x-5)) ?

The derivative of (x-3/(6x-5)) is (13)/((6x-5)^2)

What is the first derivative of (x-3/(6x-5)) ?

The first derivative of (x-3/(6x-5)) is (13)/((6x-5)^2)

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\frac{d}{d x} (\frac{x - 3}{6 x - 5})

\frac{13}{( 6 x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 3}{6 x - 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( 6 x - 5 ) - \frac{d}{d x} ( 6 x - 5 ) ( x - 3 )}{( 6 x - 5 ) ^{2}}

\frac{d}{d x} (x - 3) = 1

\frac{d}{d x} (6 x - 5) = 6

= \frac{1 \cdot ( 6 x - 5 ) - 6 ( x - 3 )}{( 6 x - 5 ) ^{2}}

Simplify

\frac{1 \cdot ( 6 x - 5 ) - 6 ( x - 3 )}{( 6 x - 5 ) ^{2}} : \frac{13}{( 6 x - 5 ) ^{2}}

= \frac{13}{( 6 x - 5 ) ^{2}}

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

\frac{\partial}{\partial y} (e^{- x} cos (y))

(2, 5), (3, 1)

\int 0.33 e^{- 0.33 y} d y

\int \frac{4}{1 + 4 x ^{2}} d x

What is the derivative of (x-3/(6x-5)) ?
The derivative of (x-3/(6x-5)) is (13)/((6x-5)^2)
What is the first derivative of (x-3/(6x-5)) ?
The first derivative of (x-3/(6x-5)) is (13)/((6x-5)^2)