Year in Review

Power Rule

d/dx [x^n]= nx^n-1

Quotient Rule

d/dx [f(x)/g(x)] = g(x)f'(x)-f(x)g'(x)/(g(x))²

Product Rule

d/dx [f(x)g’(x)+f’(x)g(x)

d/dx(sin x)

cos x

d/dx(cos x)

-sin x

d/dx(tan x)

sec² x

d/dx(csc x)

-csc x cot x

d/dx(sec x)

sec x tan x

d/dx(cot x)

-csc² x

d/dx(f^-1(a)

-a/f²

d/dx(ln x)

1/x

d/dx(log base a x)

1/ln(a)x

d/dx(c)

0

d/dx(a^x)

ln(a)*a^x

d/dx(e^x)

e^x

d/dx(x^f(x))

e^f(x) d/dx f(x)

d/dx(arcsin x) / (sin x)^-1

f’(x)/(1-(f(x))²)^1/2

d/dx(arccos x) / (cos x)^-1

-f’(x)/(1-(f(x))²)^1/2

d/dx(arctan x) / (tan x)^-1

f’(x)/1+(f(x))²

∫sin(x)dx

-cos x

∫cos(x)dx

sin x

∫sec²(x)dx

tan x

∫csc(x)cot(x)dx

∫sec(x)tan(x)dx

sec x

∫csc²(x)dx

∫e^xdx

e^x

∫a^xdx