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Popular >

d/(du)(sqrt((u-1)/(u+1)))

Solution

\frac{d}{d u} (\frac{u - 1}{u + 1})

Solution

\frac{1}{u - 1 ( u + 1 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d u} (\frac{u - 1}{u + 1})

Apply the chain rule:

\frac{1}{2 \frac{u - 1}{u + 1}} \frac{d}{d u} (\frac{u - 1}{u + 1})

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

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

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

Simplify

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

= \frac{1}{u - 1 ( u + 1 ) ^{\frac{3}{2}}}

Graph

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Frequently Asked Questions (FAQ)

What is the d/(du)(sqrt((u-1)/(u+1))) ?
The d/(du)(sqrt((u-1)/(u+1))) is 1/(sqrt(u-1)(u+1)^{3/2)}
What is the first d/(du)(sqrt((u-1)/(u+1))) ?
The first d/(du)(sqrt((u-1)/(u+1))) is 1/(sqrt(u-1)(u+1)^{3/2)}