# How do you implicitly differentiate #-1=xy^2+2x^2y-e^ycsc(3x/y) #?

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

To implicitly differentiate the equation (-1 = xy^2 + 2x^2y - e^y \csc\left(\frac{3x}{y}\right)), we'll differentiate each term with respect to (x) using the chain rule and product rule where necessary.

(\frac{d}{dx}(-1) = 0)

(\frac{d}{dx}(xy^2) = y^2 + 2xy \frac{dy}{dx})

(\frac{d}{dx}(2x^2y) = 4xy + 2x^2 \frac{dy}{dx})

(\frac{d}{dx}\left(-e^y \csc\left(\frac{3x}{y}\right)\right) = -e^y \csc\left(\frac{3x}{y}\right) \frac{d}{dx}\left(\csc\left(\frac{3x}{y}\right)\right) - e^y \cot\left(\frac{3x}{y}\right) \frac{d}{dx}\left(\frac{3x}{y}\right))

Now, we'll compute the derivatives (\frac{dy}{dx}) and (\frac{d}{dx}\left(\frac{3x}{y}\right)).

(\frac{d}{dx}\left(\frac{3x}{y}\right) = \frac{3\frac{dy}{dx}y - 3xy'}{y^2})

Now, we'll substitute the derivatives back into the equation and solve for (\frac{dy}{dx}).

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

To implicitly differentiate the equation -1=xy^2+2x^2y-e^ycsc(3x/y) with respect to (x), you would use the rules of implicit differentiation and the chain rule where necessary. The result will give you the derivative of (y) with respect to (x), denoted as (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.

- How do you differentiate #g(y) =x^2(x^2 + 6) # using the product rule?
- How do you differentiate #g(x) =e^(1-x)tanx# using the product rule?
- How do you use the product rule to differentiate #f(t) = (1 - t^2) (1 - 3/t^2)#?
- How do you differentiate #4e^y(x-y^2)=2(x-y)#?
- How do you Implicitly differentiate #e^(x/y)=x-y#?

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