Studied by 59 peoplef(x)g(x)= . .
f’(x)g(x)+f(x)g’(x) (*Product Rule*)
f(x)/g(x)= . . .
f’(x)g(x)-f(x)g’(x)/(g(x))² (*Quotient Rule*)
d/dx[f(g(x))]= . . .
f’(g(x))g’(x) (*Chain Rule*)
d/dx(cf/(x))= . . .
cf’(x)
d/dx(x^n)= . . .
nx^n-1
d/dx(f(x)__+__g(x))= . . .
f’(x)__+__g’(x)
d/dx(c)= . . .
0
d/dx(e^g(x))= . . .
g’(x)e^g(x)
d/dx[ln(g(x))]= . . .
g’(x)/g(x)
d/dx[sin(x)]= . . .
cos(x)
d/dx[cos(x)]= . . .
-sin(x)
d/dx[csc(x)] = . . .
-csc(x)cot(x)
d/dx[sec(x)]= . . .
sec(x)tan(x)
d/dx[tan(x)]= . . .
sec²(x)
d/dx[cot(x)]= . . .
-csc²(x)
d/dx[sin⁻¹(x)]= . . .
1/√1-x²
d/dx[cos⁻¹(x)]= . . .
-1/√1-x²
d/dx[csc⁻¹(x)]= . . .
-1/lxl√1-x²
d/dx[sec⁻¹(x)]= . . .
1/lxl√1-x²
d/dx[tan⁻¹(x)]= . . .
1/1+x²
d/dx[cot⁻¹(x)]= . . .
-1/1+x²
d/dx[a^x]= . . .
a^x(ln(a))
d/dx[ln(x)]= . . .
1/x, x>0
d/dx[lnlxl]= . . .
1/x, x~~=0~~
d/dx[log[a](x)]= . . .
1/x(ln(a)), x>0
d/dx[sinh(x)]= . . .
cosh(x)
d/dx[cosh(x)]= . . .
sinh(x)
d/dx[tanh(x)]= . . .
sech²(x)
d/dx[csch(x)]= . . .
-csch(x)coth(x)
d/dx[sech(x)]= . . .
-sech(x)tanh(x)
d/dx[coth(x)]= . . .
-csch²(x)
Note
Flashcard