# How do you implicitly differentiate #-1=-y^2x+xy-ye^(xy) #?

OR

Diff.ing term-wise, using the usual Rules of Diffn., we get,

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

To implicitly differentiate the equation -1=-y^2x+xy-ye^(xy):

- Differentiate each term with respect to x.
- Apply the product rule and chain rule where necessary.
- Solve for dy/dx.

Differentiating each term:

- For -1, the derivative is 0.
- For -y^2x, the derivative is -y^2 - 2yx(dy/dx).
- For xy, the derivative is y + x(dy/dx).
- For -ye^(xy), the derivative is -y^2e^(xy) - y^3x(dy/dx) - ye^(xy).

Combine the terms involving dy/dx: -2yx(dy/dx) + x(dy/dx) - y^3x(dy/dx) = -y^2 - y^2e^(xy)

Factor out dy/dx: (dy/dx)(-2yx + x - y^3x) = -y^2 - y^2e^(xy)

Solve for dy/dx: dy/dx = (-y^2 - y^2e^(xy)) / (-2yx + x - y^3x)

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 find the derivative (quotient rule) for #(x^2 + 8x + 3)/sqrtx#?
- How do you differentiate #g(x) =x^2cotx# using the product rule?
- How do you differentiate #f(x)=1/x*e^(x^2)# using the product rule?
- How do you differentiate # y =sin(ln(cos x)) # using the chain rule?
- How do you differentiate #2xy=y^2-x^2/y#?

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