DIFFERENTIATION





















f(x) = ln x f^-1(x) = e^x

y=ln(ax+b): can be defined for ax+b>0, intersects x-axis at x-coordinate: ax+b =1, asymtote: ax+b=0

Rate of change



Increasing at a steady rate: x = mt + c


Small changes
(x₁, y₁) > (x₂, y₂), δy = y₂ - y₁, δx =x₂ - x₁
dx > 0 increase in x, x₂ - x₁ > 0
dx < 0 decrease in x, x₂ - x₁ < 0





Stationery pt/ turning pt/ stationery (max/min value of y)

Stationery:-pt = (a, f(a)), -value of y = f(a)



Motion of a particle
s = dist/displacement from starting/fixed pt O
P: instantaneously at rest, v = 0



INTEGRATION








[αf(x)+ βg(x)]dx = αf(x)dx + βg(x)dx (α, β = constants)
cos x dx = sin x + c
sin x dx = -cos x + c
tan x dx = sec² x + c
cos(ax+b) dx = a^-1 sin(ax+b) + c
sin(ax+b) dx = -a^-1 cos(ax+b) + c
tan(ax+b) dx = a^-1 sec²(ax+b) + c
e^(ax+b) dx = a^-1e^(ax+b) + c (a 0)
(ax+b)^-1 dx = a^-1ln(ax+b) + c (a 0, ax+b > 0)
















Kinematics
at time t; displacement, x = v dt = a dtdt, velocity, v = a dt, (av. velocity = displacement/ time)


Amaths5
Amaths1
Amaths2
Amaths3

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