# What is the implicit derivative of #1= 3y-ysqrt(x-y) #?

You differentiate both sides of the expression

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

To find the implicit derivative of (1 = 3y - y\sqrt{x-y}), we differentiate both sides of the equation with respect to (x) using the chain rule and the product rule. Then, we solve for (\frac{dy}{dx}).

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

To find the implicit derivative of the equation (1 = 3y - y\sqrt{x - y}), you'll need to use the chain rule and implicit differentiation. Differentiate both sides of the equation with respect to (x) using the chain rule where necessary.

Starting with the given equation:

[1 = 3y - y\sqrt{x - y}]

Differentiating both sides with respect to (x):

[\frac{d}{dx}(1) = \frac{d}{dx}(3y) - \frac{d}{dx}(y\sqrt{x - y})]

Simplify and solve for (\frac{dy}{dx}).

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

- How do you find the derivative of #y =4/sqrt(x)#?
- If #f(x) =csc^3(x/2) # and #g(x) = sqrt(2x+3 #, what is #f'(g(x)) #?
- How do you differentiate #f(x)= (4 x^2 + 5x -8 )/ (x- 1 )# using the quotient rule?
- How do you differentiate #f(x)=e^(x^2)/(e^(2x)-2x)# using the quotient rule?
- How do you differentiate #f(x)=(x^2+4x)*(x^3+2x+1)# 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