At a Glance - Using Leibniz Notation
Things to remember for implicit differentiation:
- since y is a function of x, any derivative involving y must use the chain rule
- since y is a function of x, taking the derivative of xy (or of any other product involving both x and y) requires the product rule
- since y is a function of x, taking the derivative of (or any other quotient involving both x and y) requires the quotient rule
Example 1
Find given that x^{2} + y^{2} = 4. |
Example 2
Find the derivative of y with respect to x given that 4y^{2} + 8y = 2x^{2}. |
Example 3
Assuming y is a function of x and xy + x = y, find . |
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