What is the derivative of (6t+1)/(6t-1) ?

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

What is the first derivative of (6t+1)/(6t-1) ?

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

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derivative of

\frac{6 t + 1}{6 t - 1}

- \frac{12}{( 6 t - 1 ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{6 t + 1}{6 t - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d t} ( 6 t + 1 ) ( 6 t - 1 ) - \frac{d}{d t} ( 6 t - 1 ) ( 6 t + 1 )}{( 6 t - 1 ) ^{2}}

\frac{d}{d t} (6 t + 1) = 6

\frac{d}{d t} (6 t - 1) = 6

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

Simplify

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

= - \frac{12}{( 6 t - 1 ) ^{2}}

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