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)