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)|