IMPLICIT DIFFERENTIATION
"with respect to x"......
Explicit Form
can be solved for y in terms of x
Implicit Form
cannot be solved for y in terms of x
Read as, "the derivative of y with respect to x."
numerator tells what you are deriving
denominator tells what you are "respecting"
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Ex #1: When variables agree and disagree:
A.) Find the derivative of 2x3 – 4y + 5 = 0
B.) Find the derivative of 2x3 – 4y + 5 = 0
with respect to x....IMPLICITLY
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EX #2: Variables Disagree A.) Find the derivative of y 3 with respect to x.
B.) Find the derivative of 2x – 5y = 0 with respect to x
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EX #3: Find given:
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Guidelines for Implicit Differentiation
1. Differentiate both sides with respect to x.
2. Collect terms on one side equal to all other terms on the other side
3. Factor out 4. Solve for
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EX #5: Find the slope of the tangent line to the graph 2
of x2 + 4y = 4 at the point given:
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EX #6: Find implicitly of 7
EX #7: Find implicitly of 8
EX #8: Find the standard form of the equation of the tangent line to the graph of the hyperbola at the point (1, – 1). 9
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