What is the d/(dt)(sqrt((1-2t)/(1+2t))) ?

The d/(dt)(sqrt((1-2t)/(1+2t))) is -2/(sqrt(-2t+1)(2t+1)^{3/2)}

What is the first d/(dt)(sqrt((1-2t)/(1+2t))) ?

The first d/(dt)(sqrt((1-2t)/(1+2t))) is -2/(sqrt(-2t+1)(2t+1)^{3/2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d t} (\frac{1 - 2 t}{1 + 2 t}) = - \frac{4}{( 1 + 2 t ) ^{2}}

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

Simplify

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

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

- \frac{2 s + 1}{s ^{2} + 3 s + 2}

\frac{\partial}{\partial y} (x^{3} y^{6})

\int (3 x^{- 2} - 4 x^{2} + 1) d x

\frac{\partial}{\partial x} (e^{- 9 x} cos (θ))

\frac{s}{s ^{2} + 4 ^{2}}

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