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Question		Answer
(c)' start learning		0, c ∈ R
(x^p)′ start learning		px^(p−1), p ∈ R
(sin x)′ start learning		cos x, x ∈ R
(cos x)′ start learning		− sin x, x ∈ R
(tg x)′ start learning		1/(cos^2 x), x =/= π/2 + kπ, k ∈ Z
(ctg x)′ start learning		-(1/(sin^2 x)), x =/= kπ, k ∈ Z
(arcsin x)′ start learning		1/(√1-x^2), x ∈ (−1, 1)
(arccos x)′ start learning		-(1/(√1-x^2)), x ∈ (−1, 1)
(arctg x)′ start learning		1/(1+x^2), x ∈ R
(arcctg x)′ start learning		-(1/1+x^2), x ∈ R
(a^x)′ start learning		a^x ln a, a ∈ (0, 1) ∪ (1, ∞), x ∈ R
(e^x)′ start learning		e^x, x ∈ R
(log_a x)′ start learning		1/(x ln a), a ∈ (0, 1) ∪ (1, ∞), x ∈ (0, ∞)
(ln x)′ start learning		1/x, x ∈ (0, ∞)

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