Question
Find the derivative of $y$ with respect to $x, \frac{d y}{d x}$, by implicit differentiation.$$x^{2}+y^{2}=16$$
Step 1
The derivative of $x^{2}$ with respect to $x$ is $2x$ and the derivative of $y^{2}$ with respect to $x$ is $2y \frac{dy}{dx}$ by the chain rule. The derivative of a constant is zero. So we have: $$2x + 2y \frac{dy}{dx} = 0$$ Show more…
Show all steps
Your feedback will help us improve your experience
Varsha Aggarwal and 66 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. $$ x^{2}+y^{2}=16$$
Differentiation
Implicit Differentiation and Related Rates
Find $d y / d x$ by implicit differentiation. $$x^{2}-2 y^{2}=16$$
Find $d y / d x$ by implicit differentiation. $$ x^{2}-y^{2}=16 $$
Implicit Differentiation
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD