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Find (dy)/(dx) in each of the followi...

Find `(dy)/(dx)` in each of the following: `x^(2/3)+y^(2/3)=a^(2/3)`

Text Solution

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Given `x^{2 / 3}+y^{2 / 3}=a^{2 / 3}`

`y^{2 / 3}=a^{2 / 3}-x^{2 / 3}`

Differentiate w.r.t.x

`(2 / 3) y^{1 / 3} d y / d x=0-(2 / 3) x^{1 / 3}`
`d y / d x=-(2 / 3) x^{1 / 3} /(2 / 3) y^{1 / 3}`
`=-x^{1 / 3} / y^{1 / 3}`
`=-(x / y)^{1 / 3}`
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