Deriative rules AB Calc

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second deriative

acceleration

dy/dx (sin x)

cos x

dy/dx (csc x)

cscxcotx

sum and difference rule

dy/dx= f'(x) ± g'(x)

product rule

dy/dx= g(x)f'(x) + f(x)g'(x)

quotient rule

dy/dx= g(x)f'(x) - f(x)g'(x)/ (g(x)) ²

constant rule

f'(c)= 0

constant multiple rule

f'(cf(x)) = c × f'(x)

chain rule

f'(g(x)) × g'(x) -deriative of outside evaluated at the inside x derivative of the inside

power rule

f'(xⁿ)= nxⁿ⁻¹

dy/dx (sec x)

secxtanx

f'(tan x)

sec²x

uses of chain rule

used for any expression raised to a power

first deriative

velocity

dy/dx(cot x)

-csc²x

dx/dy (cos x)

-sin x

speed

Absolute value of velocity. |v(t)|


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