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If log10(x3-y3x3+Y3)=2then show that dydx=-99x2101y2 - Mathematics and Statistics

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Sum

If  `log_10((x^3-y^3)/(x^3+y^3))=2 "then show that"  dy/dx = [-99x^2]/[101y^2]`

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Solution

`log_10((x^3-y^3)/(x^3+y^3))=2`

Convert logarithmic form into exponential form,

`((x^3-y^3)/(x^3+y^3))=10^2 `

`((x^3-y^3)/(x^3+y^3))=100`

x3 - y3 = 100x3 + 100y3

∴ - 99x3 - 101y3 = 0

- 101y3 = 99x3

Differentiat ing w.r.t. x on both sides

- 99(3x2) - 101(3y2 `dy/dx`) = 0

∴ 99x2 + 101y2 `dy/dx`= 0

∴ 101y2 `dy/dx`= - 99x2

∴ `dy/dx=(-99x^2)/(101y^2)`

Concept: Derivatives of Functions in Parametric Forms
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