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derivative of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` ?

derivative of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` ?

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derivative of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` ?

Postby Integr88 » Mon 11 April, 2011 17:07

how can you take the derivatives of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` ?

Please show all steps.
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Re: derivative of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` ?

Postby barnamah » Mon 11 April, 2011 17:21

To take the derivatives of `y = (a^2 + x^2 / a^2 - x^2) ^ (1/2)` we firs rewrite the `x^2 / a^2` as `x^2*1/a^2` and we can write `1/a^2=a^-2` we have:

`y = (a^2 + x^2*a^-2 - x^2) ^ (1/2)`

I am assuming a is a constant so
I'll go term by terms:
for `a^2=0`

for `x^2*a^-2` because `a^-2` is a constant, it stays the same and we just take the derivatives of `x^2`
`2xa^-2`

for `-x^2`
`-2x`

putting them together we have:

`y'=1/2(0+2xa^-2-2x)^(1/2-1)`
`y'=1/2(2xa^-2-2x)^(3/2)` this is the final answer but if you want to write it as fraction then:

`y'=1/2(2x1/a^2-2x)^(3/2)`
Explore and know. That is asked.
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