Question
Find $d y / d x$ by implicit differentiation for the following. $$x+\ln y=x^{2} y^{3}$$
Step 1
Using the chain rule for $\ln y$ and the product rule for $x^{2} y^{3}$, we get: $$1 + \frac{1}{y} \frac{dy}{dx} = 2x y^{3} + 3x^{2} y^{2} \frac{dy}{dx}.$$ Show more…
Show all steps
Your feedback will help us improve your experience
Amy Jiang and 55 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find $d y / d x$ by implicit differentiation for the following. $$x^{2} e^{y}+y=x^{3}$$
Applications of the Derivative
Implicit Differentiation
Find $d y / d x$ by implicit differentiation for the following. $$ x^{2} e^{y}+y=x^{3} $$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD