Question

Use implicit differentiation find dy/dx of
xy^1/3+y=10

Answer 1

\[xy^{\frac{1}{3}} + y = 10\]
Differentiate both sides.

\[\frac{d}{dx} (xy^{\frac{1}{3}} + y ) = \frac{d}{dx} (10)\]
\[\frac{d}{dx} (xy^{\frac{1}{3}} ) + \frac{d}{dx} (y) = 0\]
Apply product rule and find \(\frac{dy}{dx}\).
Getting this? :)

Answer 2

U can simply do the derivative of xy^1/3 using chain rule. For y you would just write dy/dx. Then 10 is a constant so it would just be 10. At last, you solve for dy/dx.

Answer 3

ya Im getting lost somewhere after I've applied the product rule. is this right?
\[(1)(y ^{1/3}) + (x)(1/3y ^{-1/6})(dy/dx) +dy/dx=0\]