For the curve xy + x2y - xy² = 1, use implicit differentiation to find the equations of the tangent lines corresponding to the two points with x = -1.

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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For the curve xy + x²y - xy² = 1, use implicit differentiation to find the equations of the tangent lines corresponding
to the two points with x = -1.
Why do we need the Chain Rule in implicit differentiation? Show with an example and describe how the Chain Rule is
being used.
. Use logarithmic differentiation to find for y = x
dy
dx
xlux
If we did not have logarithmic differentiation, what rules would we need to use to find the derivative of
(322+4) (2-1)³
? Use logarithmic differentiation to find this derivative instead. What are the benefits of using this
y =
sin 3x cos 2x
process?
Application - Chemistry
The ideal gas law PV = nRT gives a relationship between the pressure P in pascals (you can read about the pressure unit
pascals here if you'd like ), the volume V in cubic meters, n is the number of moles of a substance present (you can read
about moles here if you'd like e) and R is the ideal gas constant (you can read about the gas constant here) and I is the
temperature in Kelvins (here's some information about the Kelvin scale).
It's worth mentioning that the ideal gas law assumes we can ignore things like the volume of individual molecules and the
attraction between particles. So if we say something like "Pretend we have an ideal gas in a box," we are quite literally
pretending, because there is no ideal gas! But this equation is a statement about the relationship of units to each other, and
thus is useful for comparing quantities in an approximate way. In practice, chemists might measure the deviation from the
ideal gas law in order to deduce information about other properties.
The tools we developed in this unit for comparing related rates can help us analyze situations involving the ideal gas
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Transcribed Image Text:WOIS Port Trait Rev... VitalSource Booksh... For the curve xy + x²y - xy² = 1, use implicit differentiation to find the equations of the tangent lines corresponding to the two points with x = -1. Why do we need the Chain Rule in implicit differentiation? Show with an example and describe how the Chain Rule is being used. . Use logarithmic differentiation to find for y = x dy dx xlux If we did not have logarithmic differentiation, what rules would we need to use to find the derivative of (322+4) (2-1)³ ? Use logarithmic differentiation to find this derivative instead. What are the benefits of using this y = sin 3x cos 2x process? Application - Chemistry The ideal gas law PV = nRT gives a relationship between the pressure P in pascals (you can read about the pressure unit pascals here if you'd like ), the volume V in cubic meters, n is the number of moles of a substance present (you can read about moles here if you'd like e) and R is the ideal gas constant (you can read about the gas constant here) and I is the temperature in Kelvins (here's some information about the Kelvin scale). It's worth mentioning that the ideal gas law assumes we can ignore things like the volume of individual molecules and the attraction between particles. So if we say something like "Pretend we have an ideal gas in a box," we are quite literally pretending, because there is no ideal gas! But this equation is a statement about the relationship of units to each other, and thus is useful for comparing quantities in an approximate way. In practice, chemists might measure the deviation from the ideal gas law in order to deduce information about other properties. The tools we developed in this unit for comparing related rates can help us analyze situations involving the ideal gas Sign out 8:45 DELL
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