What is the derivative of ((3x+1))/((x-1)) ?

The derivative of ((3x+1))/((x-1)) is -4/((x-1)^2)

What is the first derivative of ((3x+1))/((x-1)) ?

The first derivative of ((3x+1))/((x-1)) is -4/((x-1)^2)

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derivative of

\frac{( 3 x + 1 )}{( x - 1 )}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{3 ( x - 1 ) - 1 \cdot ( 3 x + 1 )}{( x - 1 ) ^{2}} : - \frac{4}{( x - 1 ) ^{2}}

= - \frac{4}{( x - 1 ) ^{2}}

2 a^{x}

(4 x^{5} + 1)^{3}

cos (x^{2} + 9)

\frac{d}{d x} (2 x^{3} - 16 x^{2} - 2 c + 4 d)

g (x) = 3^{2 x + 7}

What is the derivative of ((3x+1))/((x-1)) ?
The derivative of ((3x+1))/((x-1)) is -4/((x-1)^2)
What is the first derivative of ((3x+1))/((x-1)) ?
The first derivative of ((3x+1))/((x-1)) is -4/((x-1)^2)