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

The derivative of w/(w+d/w) is (2wd)/((w^2+d)^2)

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

The first derivative of w/(w+d/w) is (2wd)/((w^2+d)^2)

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derivative of

\frac{w}{w + \frac{d}{w}}

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

Solution steps

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

Treat

d

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (4 y - 2 x)

f (x) = 3 36 x^{2} + 10

\frac{\partial}{\partial x} (- 2 x - 8 y + 18)

\frac{d}{d x} (cos (arccos (x)))

\frac{d}{d x} (\frac{1}{2} (x - \frac{1}{2} sin (2 x)))

What is the derivative of w/(w+d/w) ?
The derivative of w/(w+d/w) is (2wd)/((w^2+d)^2)
What is the first derivative of w/(w+d/w) ?
The first derivative of w/(w+d/w) is (2wd)/((w^2+d)^2)