Differentiate f(x)=4x⁴−3x²+7.
Show a complete solution and verify with a second representation.
Unit 05 · Core Pathway
Differentiation Rules & Higher Derivatives
How do derivative rules make complex rates of change efficient, interpretable, and verifiable?
Khaemenes Academy · Calculus I
Core Practice
Differentiation Rules & Higher Derivatives · Show reasoning, notation, intervals, units, and corrections.
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Date
Differentiate 5.
Show a complete solution and verify with a second representation.
Differentiate f(x)=5x⁴−3x²+7.
Show a complete solution and verify with a second representation.
Differentiate 5.
Show a complete solution and verify with a second representation.
Differentiate (x²+1)(x³−2).
Show a complete solution and verify with a second representation.
Differentiate x^(−3).
Show a complete solution and verify with a second representation.
Differentiate cos x.
Show a complete solution and verify with a second representation.
At x=π/2, find the slope of y=sin x.
Show a complete solution and verify with a second representation.
Differentiate cos x.
Show a complete solution and verify with a second representation.
At x=π/2, find the slope of y=sin x.
Show a complete solution and verify with a second representation.
Differentiate 4^x.
Show a complete solution and verify with a second representation.
Differentiate 5e^(−2x).
Show a complete solution and verify with a second representation.
Differentiate log₁₀x.
Show a complete solution and verify with a second representation.
Why must the log argument be checked?
Show a complete solution and verify with a second representation.
When is a particle at rest?
Show a complete solution and verify with a second representation.
Explain the units of acceleration.
Show a complete solution and verify with a second representation.