Derivatives

f(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)