Calculus · College · College and University

Calculus Derivatives and Integrals Reference

Core derivative and integration rules used across intro calculus courses.

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Power rule for derivatives: d/dx[x^n] = ?

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n*x^(n-1)

Product rule: d/dx[f(x)*g(x)] = ?

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f'(x)*g(x) + f(x)*g'(x)

Quotient rule: d/dx[f(x)/g(x)] = ?

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[f'(x)*g(x) - f(x)*g'(x)] / [g(x)]^2

Chain rule: d/dx[f(g(x))] = ?

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f'(g(x)) * g'(x)

d/dx[sin(x)] = ?

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cos(x)

d/dx[cos(x)] = ?

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-sin(x)

d/dx[tan(x)] = ?

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sec^2(x)

d/dx[cot(x)] = ?

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-csc^2(x)

d/dx[sec(x)] = ?

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sec(x)*tan(x)

d/dx[csc(x)] = ?

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-csc(x)*cot(x)

d/dx[e^x] = ?

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e^x

d/dx[a^x] = ?

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a^x * ln(a)

d/dx[ln(x)] = ?

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1/x

d/dx[log_a(x)] = ?

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1/(x*ln(a))

d/dx[sin^(-1)(x)] = ?

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1/sqrt(1-x^2)

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