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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 3 lim (5^{x})

x \to 2 - lim (\frac{x ^{2}}{4 - x ^{2}})

- 4 x - \frac{676}{x}

\int x 36 + x^{2} d x

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

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