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

The d/(dt)(t/(t^2+y^2)) is (-t^2-2ty\frac{dy)/(dt)+y^2}{(t^2+y^2)^2}

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

The first d/(dt)(t/(t^2+y^2)) is (-t^2-2ty\frac{dy)/(dt)+y^2}{(t^2+y^2)^2}

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 5 lim (3 x^{2} + 5)

\frac{d}{d x} (\frac{2}{3} x^{2})

\frac{d}{d x} (\frac{c ^{6} - x ^{6}}{c ^{6} + x ^{6}})

n = 1 \sum \infty (\frac{1}{n + 1})^{2}

\int_{0}^{3} (2 x - x^{2})^{5} (1 - x) d x

What is the d/(dt)(t/(t^2+y^2)) ?
The d/(dt)(t/(t^2+y^2)) is (-t^2-2ty\frac{dy)/(dt)+y^2}{(t^2+y^2)^2}
What is the first d/(dt)(t/(t^2+y^2)) ?
The first d/(dt)(t/(t^2+y^2)) is (-t^2-2ty\frac{dy)/(dt)+y^2}{(t^2+y^2)^2}