# How do you implicitly differentiate #2= xy-ysin^2x-cos^2xy^2 #?

Use Leibniz notation and you should be fine. For the second and third terms, you have to apply chain rule a couple of times.

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

To implicitly differentiate ( 2 = xy - y\sin^2(x) - \cos^2(xy^2) ), we differentiate each term with respect to ( x ) and then solve for ( \frac{dy}{dx} ).

[ \frac{d}{dx} (2) = \frac{d}{dx} (xy) - \frac{d}{dx} (y\sin^2(x)) - \frac{d}{dx} (\cos^2(xy^2)) ]

Simplify and differentiate each term:

[ 0 = y + x\frac{dy}{dx} - y\sin(2x) - 2\cos(xy^2) \cdot (-y^2)\frac{dy}{dx} ]

Rearrange terms and solve for ( \frac{dy}{dx} ):

[ \frac{dy}{dx} (x - 2\cos(xy^2)y^2) = y\sin^2(x) - y ]

Finally,

[ \frac{dy}{dx} = \frac{y\sin^2(x) - y}{x - 2\cos(xy^2)y^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 #f(x)=1/(ln(1-(e^(-cos(x^2)))))^(3/2)# using the chain rule?
- How do you differentiate #f(x) =1/(e^(3x)-2)# using the quotient rule?
- How do you differentiate #f(x)=ln(3x^2)# using the chain rule?
- How do you differentiate #f(x)=(lnx-x)(cotx-2e^x)# using the product rule?
- How do you find the derivative of #lnx/cscx#?

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