Differentiate (x²+1)^3.
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 06 · Extended Pathway
Chain Rule, Implicit & Inverse Functions
How do nested, implicit, and inverse relationships change the way derivatives are calculated and interpreted?
Khaemenes Academy · Calculus I
Extended Practice
Chain Rule, Implicit & Inverse Functions · Show reasoning, notation, intervals, units, and corrections.
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Differentiate √(1+x³).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate ln(5x−1).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate sin(3x).
Generalize, analyze an edge case, or defend the result without relying on technology.
Identify outer and inner functions in cos(x²+4).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate ln(5x−1).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate xy=6 implicitly.
Generalize, analyze an edge case, or defend the result without relying on technology.
For x²+y²=25, find dy/dx.
Generalize, analyze an edge case, or defend the result without relying on technology.
Why does d(y²)/dx include y'?
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate arctan x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate y=(x²+1)^x in logarithmic form.
Generalize, analyze an edge case, or defend the result without relying on technology.
How is the result checked?
Generalize, analyze an edge case, or defend the result without relying on technology.