13/14/15 - differentiation/ integration Flashcards
gradient is the
rate of change of x with respect to y
differentiation notation
dy/dx
f’(x)
differentiation
y= ax^n
dy / dx = anx ^n-1
times by the power of x then -1 from the power
eg y = x^3
dy / dx = 3x^2
second order derivative
differentiate twice
f’‘(x)
d^2y/ dx^2
rate of change of the gradient of a function
summing functions
is y = f(x) + g(x)
dy/ dx = f’(x) + g’(x)
a function is increasing if
dy/dx >0
and decreasing if its <0
a point is a max / min if
max if f’‘(x) <0
min if f’‘(x) >0
if second order deriveative = 0 could be max/ min or inflection point
integration
S y= ax^n
dx = a/(n+1) x ^n+1 + c
add one to the power and divide by new power
integration notation
S (equation) dx = (integrated form) +c
if definite write in [ ] with limits outside