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Popular >

d/(dt)(1/(1+t^2))

Solution

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

Solution

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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