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Flip to reveal answersWhat is the power rule for d/dx(xⁿ)?
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All 8 Flashcards — Standard derivatives
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Question
What is the power rule for d/dx(xⁿ)?
Answer
n·x^(n−1) — bring the power down as a multiplier, then reduce the power by 1.
Question
Derivative of a constant?
Answer
0 — a constant graph is a flat horizontal line, so its gradient is 0.
Question
d/dx(sin x) and d/dx(cos x)?
Answer
sin x → cos x; cos x → −sin x (mind the minus). x must be in radians.
Question
d/dx(eˣ)?
Answer
eˣ — the exponential function is its own derivative.
Question
d/dx(ln x)?
Answer
1/x.
Question
How do you differentiate √x?
Answer
Rewrite as x^(1/2); then it becomes ½x^(−1/2) = 1/(2√x).
Question
How do you find the gradient of f at x = a?
Answer
Compute f′(x), then substitute: gradient = f′(a).
Question
Equation of the tangent at x = a?
Answer
y − f(a) = f′(a)(x − a), where f′(a) is the gradient and (a, f(a)) is the point.
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Full study notes for Standard derivatives
Topic 5.9 hub
Differentiation rules (HL only)
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