Differentiation Flashcards
Meaning of f’(x)<0
decreasing function
Meaning of f’(x)=0
stationary function
Meaning of f’(x)>0
increasing function
Meaning of f’‘(x)<0
Concave
Maximum
Meaning of f’‘(x)=0
point of inflection
Meaning of f’‘(x)>0
Convex
Minimum
Differentiate axn
an xn-1
Differentiate ax
lna ax
Differentiate ex
ex
Differentiate e3x
3e3x
Differentiate lnx
1/x
Differentiate sinx
cosx
Differentiate cosx
-sinx
Differentiate tanx (FB)
sec2x
Differentiate secx (FB)
secx tanx
Differentiate cotx (FB)
-cosec2x
Differentiate cosecx (FB)
-cosecxcotx
Product rule: f(x)g(x)
f’(x)g(x) + f(x)g’(x)
Implicit Diff: f(y) =
f’(y) * dy/dx
Chain rule: f(…..) =
f’(…..) * (…..)’
Reciprocal =
1/gradient or dx/dy
Parametric Differentiation
(dy/dx) = (dy/dt) x (dt/dx)