# How do you differentiate #sqrt (1-x^4) + sqrt (1-y^4)= k(x^2-y^2)#?

Writing as:

Differentiating:

Expanding and rewriting:

Personally, this is as far as I want to go, but we can "simplify" by getting common denominators:

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To differentiate the equation ( \sqrt{1-x^4} + \sqrt{1-y^4} = k(x^2-y^2) ) with respect to ( x ) and ( y ), you can follow these steps:

- Square both sides of the equation.
- Differentiate both sides with respect to ( x ) and ( y ) separately.
- Solve for ( \frac{dy}{dx} ) and ( \frac{dx}{dy} ).

This process involves some algebraic manipulations and differentiation techniques such as the chain rule and implicit differentiation.

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