# How do you differentiate #-1=xy^3-x^2y#?

Rearrange this to get dy/dx on one side of the equation:

And, thus our final solution.

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

To differentiate (-1 = xy^3 - x^2y):

- Differentiate each term of the equation with respect to (x).
- Use the product rule and chain rule where necessary.
- Collect terms involving (dy/dx) on one side and terms involving (y) and (x) on the other side.
- Solve for (dy/dx).

The derivative of the given equation with respect to (x) is:

[y^3 + 3xy^2\frac{dy}{dx} - 2xy - x^2\frac{dy}{dx} = 0]

Solve for (\frac{dy}{dx}):

[\frac{dy}{dx} = \frac{y^3 - 2xy}{2xy - x^2}]

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.

- How do you differentiate #g(t)=(2/t+t^5)(t^3+1)# using the product rule?
- How do you implicitly differentiate #2=e^(x-y)/tan(y)#?
- How do you integrate #y=(3x^4+5x^3-5)/(2x^4-4)# using the quotient rule?
- How do you differentiate #f(x) = sqrt(sin(4x) # using the chain rule?
- How do you differentiate #f(x)=(x+sinx)(lnx-x)# using the product rule?

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