Differentiate (x²+1)^3.
Show a complete solution and verify with a second representation.
Unit 06 · Core 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
Core Practice
Chain Rule, Implicit & Inverse Functions · Show reasoning, notation, intervals, units, and corrections.
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Date
Differentiate ln(5x−1).
Show a complete solution and verify with a second representation.
Differentiate (x²+1)^4.
Show a complete solution and verify with a second representation.
Differentiate ln(5x−1).
Show a complete solution and verify with a second representation.
Differentiate sin(3x).
Show a complete solution and verify with a second representation.
Differentiate √(1+x³).
Show a complete solution and verify with a second representation.
Differentiate sin(3x).
Show a complete solution and verify with a second representation.
Differentiate √(1+x³).
Show a complete solution and verify with a second representation.
Find the slope of x²+y²=25 at (3,4).
Show a complete solution and verify with a second representation.
Why does d(y²)/dx include y'?
Show a complete solution and verify with a second representation.
Find the slope of x²+y²=25 at (3,4).
Show a complete solution and verify with a second representation.
Why does d(y²)/dx include y'?
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Differentiate arctan x.
Show a complete solution and verify with a second representation.
Differentiate arccos x.
Show a complete solution and verify with a second representation.
Why take logarithms of a large product?
Show a complete solution and verify with a second representation.
How is the result checked?
Show a complete solution and verify with a second representation.