Hi there!
We can use implicit differentiation with respect to x:
If a term with 'y' is differentiated, a 'dy/dx' must be included.
We can differentiate each term separately for the explanation.
<u>3xy</u>
We must use the power rule since 'x' and 'y' are both in this term.
Power rule:
Now, we can do the others.
<u>4x</u>
This is a normal power rule derivative.
<u>y²</u>
Since we are not differentiating with respect to y, we must include 'dy/dx'.
Combine the above:
Rearrange to solve for dy/dx.
Move dy/dx to one side:
Factor out dy/dx and divide:
D. American Council on Education
Hope this helps :)
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