Unit 2: Definition of Derivatives/Basic Derivatives

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22 Terms

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Average Rate of Change of f(x) on [a,b]

f(b)-f(a)/b-a

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Instantaneous Rate of Change/Slope of tangent line/derivative (with h)

lim h->0 f(a+h)-f(a)/h

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Instantaneous Rate of Change/Slope of tangent lint/derivative (with x)

lim x->a f(x)-f(a)/x-a

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Definition of the Derivative

f'(x) = lim h->0 f(x+h)-f(x)/h

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Equation of the Tangent Line

y-y1=m(x-x1); also point-slope form where m=derivative

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Equation of the Normal Line

y-y1=1/m(x-x1)

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Definition of a Vertical Tangent Line

lim h->0 f(c+h)-f(c)/h = +/- infinity

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Derivative of a Constant

0

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Derivative of f(x) = ax

a

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Derivative of f(x) = x^n

nx^(n-1)

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Derivative of Sinx

cosx

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Derivative of cosx

-sinx

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Derivative of e^x

e^x

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Derivative of lnx

1/x

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Derivative of a^x

a^xlna

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Derivative of loga(x)

1/xlna

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Product Rule

vdu + udv

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Quotient Rule

vdu-udv/v^2

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Derivative of tanx

sec^2x

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Derivative of cotx

-csc^2x

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Derivative of secx

secxtanx

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Derivative of cscx

-cscxcotx