022 Sample Final A, Problem 4

From Math Wiki
Revision as of 16:13, 4 June 2015 by MathAdmin (talk | contribs) (Created page with " <span class="exam"> Use implicit differentiation to find <math>\frac{dy}{dx}: \qquad x+y = x^3y^3</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" !...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search


Use implicit differentiation to find

Foundations:  
When we use implicit differentiation, we combine the chain rule with the fact that is a function of , and could really be written as Because of this, the derivative of with respect to requires the chain rule, so
    
For this problem we also need to use the product rule.

Solution:

Step 1:  
First, we differentiate each term separately with respect to and apply the product rule on the right hand side to find that   differentiates implicitly to
.
Step 2:  
Now we need to solve for and doing so we find that
Final Answer:  

Return to Sample Exam