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Math Formula Encyclopedia

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134 formulas10 subjectsExamples + variables

15 matching formulas

Calculus

Derivative Definition

f′(x)=lim(h→0)[f(x+h)−f(x)]/h

Defines instantaneous rate of change.

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Calculus

Power Rule

d/dx(x^n)=n x^(n−1)

Derivative of a power function.

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Calculus

Product Rule

(fg)′ = f′g + fg′

Derivative of a product.

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Calculus

Quotient Rule

(f/g)′=(f′g−fg′)/g²

Derivative of a quotient.

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Calculus

Chain Rule

d/dx f(g(x)) = f′(g(x))g′(x)

Derivative of a composite function.

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Calculus

Integral Power Rule

∫x^n dx = x^(n+1)/(n+1)+C

Antiderivative of a power.

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Calculus

Fundamental Theorem of Calculus

∫ₐᵇ f(x)dx = F(b)−F(a)

Connects definite integrals with antiderivatives.

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Calculus

Average Rate of Change

[f(b)−f(a)]/(b−a)

Slope of a secant line over an interval.

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Calculus

Average Value of a Function

f_avg=(1/(b−a))∫ₐᵇf(x)dx

Mean value of a continuous function over an interval.

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Calculus

Derivative of e^x

d/dx(e^x)=e^x

Common reference identity or relationship used in calculus.

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Calculus

Derivative of ln x

d/dx(ln x)=1/x

Common reference identity or relationship used in calculus.

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Calculus

Derivative of sin x

d/dx(sin x)=cos x

Common reference identity or relationship used in calculus.

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Calculus

Derivative of cos x

d/dx(cos x)=−sin x

Common reference identity or relationship used in calculus.

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Calculus

Integral of 1/x

∫(1/x)dx=ln|x|+C

Common reference identity or relationship used in calculus.

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Calculus

Integral of e^x

∫e^x dx=e^x+C

Common reference identity or relationship used in calculus.

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