# How do you find the derivative of #x+xy=y^2#?

I assume that you want the derivative of

We have 3 terms and we will differentiate term-by-term.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the derivative of ( x + xy = y^2 ), you can use implicit differentiation.

First, differentiate each term with respect to ( x ) using the chain rule for terms involving ( y ).

The derivative of ( x ) with respect to ( x ) is ( 1 ). The derivative of ( xy ) with respect to ( x ) is ( y + x \frac{dy}{dx} ). The derivative of ( y^2 ) with respect to ( x ) is ( 2y \frac{dy}{dx} ).

Rearrange terms to solve for ( \frac{dy}{dx} ), the derivative of ( y ) with respect to ( x ).

[ 1 + y + x \frac{dy}{dx} = 2y \frac{dy}{dx} ]

[ 1 + y = (2y - x) \frac{dy}{dx} ]

[ \frac{dy}{dx} = \frac{1 + y}{2y - x} ]

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7