Texts: Let f(x) be defined implicitly by the equation ln(6y) = xy. 1. Use implicit differentiation to find the first derivative of y with respect to x. 2. Use implicit differentiation to find the second derivative of y with respect to x. 3. Find the point on the curve where the second derivative = 0.
Added by Angela R.
Step 1
The derivative of ln(6y) with respect to x is (1/6y) * (dy/dx) by the chain rule. The derivative of xy with respect to x is y + x(dy/dx) by the product rule. So, the equation becomes (1/6y) * (dy/dx) = y + x(dy/dx). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Varsha Aggarwal and 99 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
Use implicit differentiation to find the derivative of $y$ with respect to $x$ at the given point. $$ x y=2 ;(-2,-1) $$
Derivatives
Implicit Differentiation
Use implicit differentiation to find the derivative of $y$ with respect to $x$. $$ x^{2}=y^{2} /\left(y^{2}-1\right) $$
Use implicit differentiation to find the derivative of $y$ with respect to $x$. $$ y^{2}+y=(1+x) /(1-x) $$
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