What is the d/(dt)((1-3t^2)/(1-2t)) ?

The d/(dt)((1-3t^2)/(1-2t)) is (6t^2-6t+2)/((1-2t)^2)

What is the first d/(dt)((1-3t^2)/(1-2t)) ?

The first d/(dt)((1-3t^2)/(1-2t)) is (6t^2-6t+2)/((1-2t)^2)

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\frac{d}{d t} (\frac{1 - 3 t ^{2}}{1 - 2 t})

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

Solution steps

\frac{d}{d t} (\frac{1 - 3 t ^{2}}{1 - 2 t})

Apply the Quotient Rule:

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

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

\frac{d}{d t} (1 - 3 t^{2}) = - 6 t

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

= \frac{( - 6 t ) ( 1 - 2 t ) - ( - 2 ) ( 1 - 3 t ^{2} )}{( 1 - 2 t ) ^{2}}

Simplify

\frac{( - 6 t ) ( 1 - 2 t ) - ( - 2 ) ( 1 - 3 t ^{2} )}{( 1 - 2 t ) ^{2}} : \frac{6 t ^{2} - 6 t + 2}{( 1 - 2 t ) ^{2}}

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

What is the d/(dt)((1-3t^2)/(1-2t)) ?
The d/(dt)((1-3t^2)/(1-2t)) is (6t^2-6t+2)/((1-2t)^2)
What is the first d/(dt)((1-3t^2)/(1-2t)) ?
The first d/(dt)((1-3t^2)/(1-2t)) is (6t^2-6t+2)/((1-2t)^2)