Differentiate f(x)=4x⁴−3x²+7.
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 05 · Extended Pathway
Differentiation Rules & Higher Derivatives
How do derivative rules make complex rates of change efficient, interpretable, and verifiable?
Khaemenes Academy · Calculus I
Extended Practice
Differentiation Rules & Higher Derivatives · Show reasoning, notation, intervals, units, and corrections.
Name
Date
Differentiate x^(−3).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate 5.
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate (x²+1)(x³−2).
Generalize, analyze an edge case, or defend the result without relying on technology.
How can a symbolic derivative be checked?
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate 3sin x−2cos x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate tan x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate e^x.
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate 5e^(−2x).
Generalize, analyze an edge case, or defend the result without relying on technology.
Differentiate log₁₀x.
Generalize, analyze an edge case, or defend the result without relying on technology.
For the same s(t), find a(t).
Generalize, analyze an edge case, or defend the result without relying on technology.
Explain the units of acceleration.
Generalize, analyze an edge case, or defend the result without relying on technology.