# How do you find #dy/dx# by implicit differentiation given #y=sqrt(xy+1)#?

Square both sides to eliminate the need to use the chain rule.

Now use implicit differentiation and the product rule to find the derivative.

Hopefully this helps!

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

To find ( \frac{dy}{dx} ) by implicit differentiation for the equation ( y = \sqrt{xy + 1} ), follow these steps:

- Differentiate both sides of the equation with respect to ( x ).
- Apply the chain rule when differentiating ( \sqrt{xy + 1} ).
- Solve for ( \frac{dy}{dx} ) after differentiating each term.

The result will be:

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

Then, solve for ( \frac{dy}{dx} ).

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