# How do you differentiate #ycosx^2-y^2=xy#?

Firstly, let's apply the derivative operator to both sides, I'll try my best to colour code the use of the product rule:

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To differentiate the equation ( y \cos(x^2) - y^2 = xy ) with respect to ( x ), you'll use the implicit differentiation technique.

First, differentiate each term of the equation with respect to ( x ), then solve for ( \frac{{dy}}{{dx}} ). The steps are as follows:

- Differentiate ( y \cos(x^2) ) using the product rule.
- Differentiate ( -y^2 ) with respect to ( x ).
- Differentiate ( xy ) using the product rule.
- Combine the results and solve for ( \frac{{dy}}{{dx}} ).

Applying these steps will give you the derivative of ( y ) with respect to ( x ), ( \frac{{dy}}{{dx}} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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