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

The derivative of (5x+1)/(5x-1) is -(10)/((5x-1)^2)

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

The first derivative of (5x+1)/(5x-1) is -(10)/((5x-1)^2)

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derivative of

\frac{5 x + 1}{5 x - 1}

- \frac{10}{( 5 x - 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} (5 x + 1) = 5

\frac{d}{d x} (5 x - 1) = 5

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

Simplify

\frac{5 ( 5 x - 1 ) - 5 ( 5 x + 1 )}{( 5 x - 1 ) ^{2}} : - \frac{10}{( 5 x - 1 ) ^{2}}

= - \frac{10}{( 5 x - 1 ) ^{2}}

y = x, y = x^{6}

y^{^{'}} + \frac{2 y}{x} = 4 x

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

12 (t + 1) \frac{d y}{d t} - 9 y = 27 t

cos (4) x^{3}

What is the derivative of (5x+1)/(5x-1) ?
The derivative of (5x+1)/(5x-1) is -(10)/((5x-1)^2)
What is the first derivative of (5x+1)/(5x-1) ?
The first derivative of (5x+1)/(5x-1) is -(10)/((5x-1)^2)