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Popular >

derivative of t/(1+t^2)

Solution

derivative of

\frac{t}{1 + t ^{2}}

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d t}{d t} = 1

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of t/(1+t^2) ?
The derivative of t/(1+t^2) is (1-t^2)/((1+t^2)^2)
What is the first derivative of t/(1+t^2) ?
The first derivative of t/(1+t^2) is (1-t^2)/((1+t^2)^2)