Calc BC basic derivative rules

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16 Terms

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Constant rule

d/dx (constant) = 0

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Power rule

d/dx (axⁿ) = naxⁿ⁻¹

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Sum/difference rule

d/dx [f(x) + g(x)] = f'(x) + g'(x)

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Product rule

d/dx [f(x)*g(x)] = f(x)g'(x) + f'(x)g(x)

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Quotient rule

d/dx [f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)²]

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Derivative of Sin

d/dx sin(x) = cos(x)

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Derivative of Cos

d/dx cos(x) = -sin(x)

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Derivative of Tan

d/dx tan(x) = sec²(x)

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Derivative of Cot

d/dx cot(x) = -csc²(x)

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Derivative of Csc

d/dx csc(x) = -csc(x)cot(x)

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Chain rule

d/dx [f(g(x)] = f'(g(x))*g'(x)

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Exponential Func. Rule

d/dx eⁿ = n'(eⁿ)

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Natural Log Func. Rule

d/dx ln x = 1/x

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Limit Definition

lim (h→0) = [f(x+h) - f(x)]/[h]

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Concave up

f’’(x) > 0 (slope increasing)

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Concave down

f’’(x) < 0 (slope decreasing)