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

The derivative of w/(w+c/w) is (2cw)/((w^2+c)^2)

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

The first derivative of w/(w+c/w) is (2cw)/((w^2+c)^2)

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derivative of

\frac{w}{w + \frac{c}{w}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d w}{d w} = 1

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

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

Simplify

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

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

y = x^{2} - 6, at x = a

\frac{x ^{2} - 4}{x - 3}

\frac{d}{d θ} (1 - 2 sin (θ))

x 7^{x}

f (x) = 18 x^{3} - x

What is the derivative of w/(w+c/w) ?
The derivative of w/(w+c/w) is (2cw)/((w^2+c)^2)
What is the first derivative of w/(w+c/w) ?
The first derivative of w/(w+c/w) is (2cw)/((w^2+c)^2)