Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy = 8 (a) Find dy/dt, given x = 6 and dx/dt = 13. (b) Find dx/dt, given x = 1 and dy/dt = –6.
Added by Alfonso J.
Step 1
Step 1:** Differentiate the given equation $xy = 8$ implicitly with respect to $t$: $$x\frac{dy}{dt} + y\frac{dx}{dt} = 0$$ ** Show more…
Show all steps
Close
Your feedback will help us improve your experience
Mukesh Devi and 92 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
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = √x (a) Find dy/dt, given x = 1 and dx/dt = 6. dy/dt = (b) Find dx/dt, given x = 64 and dy/dt = 7. dx/dt =
Maitreya E.
Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy = 8. (a) Find dy/dt, given x = 2 and dx/dt = 15. dy/dt = (b) Find dx/dt, given x = 1 and dy/dt = -7. dx/dt =
Shaiju T.
Suppose that $x$ and $y$ are both differentiable functions of $t$ and are related by the given equation. Use implicit differentiation with respect to $t$ to determine $\frac{d y}{d t}$ in terms of $x, y$ and $\frac{d x}{d t}$. $$y^{2}=8+x y$$
Techniques of Differentiation
Implicit Differentiation and Related Rates
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD