lesonmathfonction.py

Created on January 02, 2022
996 Bytes
f(x)          f'(x)
x**n          nx**n-1
sqrtx         1/ 2sqrtx
cosx          -sinx
cos(ax+b)     -a*sin(ax+b)
1/x           -1/x**2
1/x**n        -n/x
lnx           1/x
e**x          e**x
e**ax+b       a*e**ax+b
sinx          cosx
sin(ax+b)     a*cos(ax+b)

u+v           u'+v'
k*u           k*u'
u*v           u'*v+u*v'
u**2          2*u'*u
u**n          n*u'* u**n-1
e**u          u'* e**u 
cosu          -u'sinu
sinu          u'cosu
1/v           -v'/v**2
1/x**n        u'*v-u*v'/ v**2 
sqrtu         u'/2sqrtu
lnu           u'/u


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e**0=1        ln(1)=0
e**1=e        lne=1
e**x*e**y = e**x+y     ln(x*y)=ln(x)+ln(y)
e**x/e**y = e**x-y     ln(x/y)=lnx-lny 
1/e**x = e**-x         ln(1/x)=-lnx
(e**x)**y= e**x*y      lnx**n=n*lnx
a**x * b**x = (a*b)**x ;  a**x/b**x = (a/b)**x
lnsqrtx= lnx**0,5
e**lnx = x      lne**x=x
e**a=e**b   a=b            ln(a)=ln(b)
e**a<e**b               ln(a)<ln(b)


log(x)=lnx/ln10    a**x=e**xlna  
x**a=e**alnx