Derivatives + Integrals

This is all the derivatives and integrals you should memorize for BC

Chain Rule ⋅

Chain Rule ⋅

(d/dx) f(g(x)) = f’(g(x)) ⋅ g’(x)

Product Rule ⋅

(d/dx) (f ⋅ g) = (f ⋅ g’) + (f’ ⋅ g)

Quotient Rule ⋅

(d/dx) (f/g) = ((g ⋅ f’) - (f ⋅ g’))/g²

Differentiation ⋅

The process of finding the derivative of a function, which measures how a function changes as its input changes.

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nu^(n-1) du/dx

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e^u du/dx

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a^u ⋅ ln(a) du/dx

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1/u du/dx

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1/(u⋅ln(b)) du/dx

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cos(u) du/dx

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-sin(u) du/dx

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sec²u du/dx

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-csc²(u) du/dx

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sec(u)tan(u) du/dx

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cot(u)csc(u) du/dx

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1/(sqrt(1-u²)) du/dx

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1/(1+u²) du/dx

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1/((u)(sqrt(1-u²))) du/dx

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1/(n+1) ⋅ u^(n+1) + C

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e^u + c

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(a^u)/(ln(a)) + C

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ln|u| + C

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(1/a) ⋅ ln|au+b| + C

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sin(u) + C

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-cos(u) + C

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tan(u) + C

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-cot(u) + C

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sec(u) + C

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-csc(u) + C

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arcsin(u) + C

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arctan(u) + C

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arcsec(u) + C

What does LIPET stand for?

Logarithms, Inverse Trig, Polynomials, Exponents, Trig

How do you do integration by parts?