What is the derivative of v/(v+c/v) ?

The derivative of v/(v+c/v) is (2cv)/((v^2+c)^2)

What is the first derivative of v/(v+c/v) ?

The first derivative of v/(v+c/v) is (2cv)/((v^2+c)^2)

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derivative of

\frac{v}{v + \frac{c}{v}}

\frac{2 c v}{( v ^{2} + c ) ^{2}}

Solution steps

\frac{d}{d v} (\frac{v}{v + \frac{c}{v}})

Apply the Quotient Rule:

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

= \frac{\frac{d v}{d v} ( v + \frac{c}{v} ) - \frac{d}{d v} ( v + \frac{c}{v} ) v}{( v + \frac{c}{v} ) ^{2}}

\frac{d v}{d v} = 1

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

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

Simplify

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

= \frac{2 c v}{( v ^{2} + c ) ^{2}}

\int_{0}^{1} e^{- 5 x^{2}} d x

x \to \infty lim (e^{\frac{1}{2} - \frac{1}{x ^{2}}} - 1)

n = 1 \sum \infty 1 (\frac{1}{6})^{n}

n = 1 \sum \infty n^{n} (x - 3)^{n}

\int_{0}^{\frac{π}{2}} \frac{cos ( θ )}{1 + sin ( θ )} d θ

What is the derivative of v/(v+c/v) ?
The derivative of v/(v+c/v) is (2cv)/((v^2+c)^2)
What is the first derivative of v/(v+c/v) ?
The first derivative of v/(v+c/v) is (2cv)/((v^2+c)^2)