What is the derivative of (-x)/((x-1)) ?

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

What is the first derivative of (-x)/((x-1)) ?

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

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derivative of

\frac{- x}{( x - 1 )}

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

Solution steps

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

Simplify

\frac{- x}{x - 1} : - \frac{x}{x - 1}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

- \frac{1 \cdot ( x - 1 ) - 1 \cdot x}{( x - 1 ) ^{2}} : \frac{1}{( x - 1 ) ^{2}}

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

\frac{d}{d x} (cos^{2} (y) - sin^{2} (x))

f (x) = (6 x^{2} + 7 x)^{4}

y = \frac{3 x \cdot 5 + 2}{x}

y = (x^{3} + 3)^{4}

3 x^{5} + 2 x^{3} + 5 x

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