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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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