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Popular >

((5-v^2)/(5+v^2))^'

Solution

(\frac{5 - v ^{2}}{5 + v ^{2}})^{^{'}}

Solution

- \frac{20 v}{( 5 + v ^{2} ) ^{2}}

Solution steps

(\frac{5 - v ^{2}}{5 + v ^{2}})^{'}

Apply the Quotient Rule:

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

= \frac{( 5 - v ^{2} ) ^{^{'}} ( 5 + v ^{2} ) - ( 5 + v ^{2} ) ^{^{'}} ( 5 - v ^{2} )}{( 5 + v ^{2} ) ^{2}}

(5 - v^{2})^{'} = - 2 v

(5 + v^{2})^{'} = 2 v

= \frac{( - 2 v ) ( 5 + v ^{2} ) - 2 v ( 5 - v ^{2} )}{( 5 + v ^{2} ) ^{2}}

Simplify

\frac{( - 2 v ) ( 5 + v ^{2} ) - 2 v ( 5 - v ^{2} )}{( 5 + v ^{2} ) ^{2}} : - \frac{20 v}{( 5 + v ^{2} ) ^{2}}

= - \frac{20 v}{( 5 + v ^{2} ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the ((5-v^2)/(5+v^2))^' ?
The ((5-v^2)/(5+v^2))^' is -(20v)/((5+v^2)^2)
What is the first ((5-v^2)/(5+v^2))^' ?
The first ((5-v^2)/(5+v^2))^' is -(20v)/((5+v^2)^2)