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Introduction to Computing Derivatives - At A Glance:
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
Find given that
x2 + y2 = 4.
Find the derivative of y with respect to x given that
4y2 + 8y = 2x2.
Assuming y is a function of x and
xy + x = y,