Given (x – 1)2 = 50, select the values of x.

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limitbreak7897

20.11.2020

Mathematics

Using implicit differentiation:

$y={ x }^{ -5 }\\ \\ y=\frac { 1 }{ { x }^{ 5 } } \\ \\ { x }^{ 5 }\cdot y=\frac { 1 }{ { x }^{ 5 } } \cdot { x }^{ 5 }$

$\\ \\ { x }^{ 5 }\cdot y=1\\ \\ { x }^{ 5 }\frac { dy }{ dx } +5{ x }^{ 4 }\cdot y=0$

$\\ \\ { x }^{ 5 }\frac { dy }{ dx } =-5{ x }^{ 4 }\cdot y\\ \\ { x }^{ 5 }\frac { dy }{ dx } =-5{ x }^{ 4 }\cdot \frac { 1 }{ { x }^{ 5 } }$

$\\ \\ \frac { 1 }{ { x }^{ 5 } } \cdot { x }^{ 5 }\frac { dy }{ dx } =-5{ x }^{ 4 }\cdot \frac { 1 }{ { x }^{ 5 } } \cdot \frac { 1 }{ { x }^{ 5 } }$

$\\ \\ \frac { dy }{ dx } =-\frac { 5{ x }^{ 4 } }{ { x }^{ 10 } } \\ \\ =-\frac { 5 }{ { x }^{ 6 } }$

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