What is the derivative of sqrt(t/(t^2+7)) ?

The derivative of sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}

What is the first derivative of sqrt(t/(t^2+7)) ?

The first derivative of sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}

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derivative of

\frac{t}{t ^{2} + 7}

\frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (\frac{t}{t ^{2} + 7})

Apply the chain rule:

\frac{1}{2 \frac{t}{t ^{2} + 7}} \frac{d}{d t} (\frac{t}{t ^{2} + 7})

= \frac{1}{2 \frac{t}{t ^{2} + 7}} \frac{d}{d t} (\frac{t}{t ^{2} + 7})

\frac{d}{d t} (\frac{t}{t ^{2} + 7}) = \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}}

= \frac{1}{2 \frac{t}{t ^{2} + 7}} \cdot \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}}

Simplify

\frac{1}{2 \frac{t}{t ^{2} + 7}} \cdot \frac{- t ^{2} + 7}{( t ^{2} + 7 ) ^{2}} : \frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

= \frac{- t ^{2} + 7}{2 t ( t ^{2} + 7 ) ^{\frac{3}{2}}}

\frac{d x}{d t} + 4 t x = t, x (0) = 0

\int \frac{x}{7} 49 + x^{2} d x

\frac{d}{d x} (e^{- 2 x} - x)

\int (4 x - 3)^{9} d x

\frac{\partial}{\partial y} (y^{3} cos (4 x))

What is the derivative of sqrt(t/(t^2+7)) ?
The derivative of sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}
What is the first derivative of sqrt(t/(t^2+7)) ?
The first derivative of sqrt(t/(t^2+7)) is (-t^2+7)/(2sqrt(t)(t^2+7)^{3/2)}