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Flip to reveal answersState the power rule for differentiation.
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All 9 Flashcards — Differentiating powers
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Question
State the power rule for differentiation.
Answer
d/dx(xⁿ) = n·xⁿ⁻¹ — multiply by the power, then reduce the power by 1.
Question
What is the derivative of a constant?
Answer
0.
Question
How do you differentiate a·xⁿ (constant multiple)?
Answer
a·n·xⁿ⁻¹ — the constant stays and multiplies.
Question
How do you differentiate a polynomial?
Answer
Differentiate each term separately (term by term), keeping the signs.
Question
Derivative of 4x?
Answer
4 (since 4x = 4x¹ → 4·1·x⁰ = 4).
Question
How do you differentiate 1/xⁿ?
Answer
Rewrite as x⁻ⁿ, then apply the power rule.
Question
Derivative of 1/x?
Answer
x⁻¹ → −x⁻² = −1/x².
Question
How do you differentiate √x?
Answer
Write √x = x^(1/2); derivative ½x^(−1/2) = 1/(2√x).
Question
Common sign slip with negative powers?
Answer
Forgetting that subtracting 1 makes the power more negative (e.g. −2 → −3).
Read the notes
Full study notes for Differentiating powers
Topic 5.3 hub
Differentiating polynomials
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