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

The derivative of (sqrt(x))/(6x-6) is -(x+1)/(12sqrt(x)(x-1)^2)

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

The first derivative of (sqrt(x))/(6x-6) is -(x+1)/(12sqrt(x)(x-1)^2)

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derivative of

\frac{x}{6 x - 6}

- \frac{x + 1}{12 x ( x - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

\frac{\frac{1}{2 x} ( 6 x - 6 ) - 6 x}{( 6 x - 6 ) ^{2}} : - \frac{x + 1}{12 x ( x - 1 ) ^{2}}

= - \frac{x + 1}{12 x ( x - 1 ) ^{2}}

\frac{d}{d x} (∣ x ∣^{3})

\int \frac{1}{( 4 x - x ^{2} ) ^{3}} d x

\int e^{- t (a + s)} d t

\int_{50}^{50.25} 2 d x

f (x) = 2 x^{5}

What is the derivative of (sqrt(x))/(6x-6) ?
The derivative of (sqrt(x))/(6x-6) is -(x+1)/(12sqrt(x)(x-1)^2)
What is the first derivative of (sqrt(x))/(6x-6) ?
The first derivative of (sqrt(x))/(6x-6) is -(x+1)/(12sqrt(x)(x-1)^2)