What is the derivative of y=((5x+9))/((x-1)) ?

The derivative of y=((5x+9))/((x-1)) is -(14)/((x-1)^2)

What is the first derivative of y=((5x+9))/((x-1)) ?

The first derivative of y=((5x+9))/((x-1)) is -(14)/((x-1)^2)

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derivative of

y = \frac{( 5 x + 9 )}{( x - 1 )}

- \frac{14}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 x + 9}{x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 x + 9 ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) ( 5 x + 9 )}{( x - 1 ) ^{2}}

\frac{d}{d x} (5 x + 9) = 5

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

= \frac{5 ( x - 1 ) - 1 \cdot ( 5 x + 9 )}{( x - 1 ) ^{2}}

Simplify

\frac{5 ( x - 1 ) - 1 \cdot ( 5 x + 9 )}{( x - 1 ) ^{2}} : - \frac{14}{( x - 1 ) ^{2}}

= - \frac{14}{( x - 1 ) ^{2}}

y = x^{3} + x^{2} + x + 1

\frac{1}{g}

(x - 2)^{3}

tan^{2} (x) - sin^{3} (x)

e^{x} + 3 x^{2}

What is the derivative of y=((5x+9))/((x-1)) ?
The derivative of y=((5x+9))/((x-1)) is -(14)/((x-1)^2)
What is the first derivative of y=((5x+9))/((x-1)) ?
The first derivative of y=((5x+9))/((x-1)) is -(14)/((x-1)^2)