Derivative Rules

d/dx xⁿ (Power Rule)

nx^(n-1)

d/dx (uv) (Product Rule)

uv' + vu'

d/dx (u/v) (Quotient Rule)

(vu'-uv')/v²

d/dx (f(g(x))) (Chain Rule)

f'(g(x)) * g'(x)

d/dx sinx

cosx

d/dx cosx

-sinx

d/dx tanx

(secx)^2

d/dx secx

secxtanx

d/dx cscx

-cscxcotx

d/dx cotx

-(cscx)²

dy/dx x=f(t) y=g(t) (parametric 1st)

(dy/dt)/(dx/dt)

d²/(dx)² x=f(t) y=g(t) (parametric 2nd)

(d/dt (dy/dx))/(dx/dt)

g(x) = f⁻¹(x) where (a,b) lies on g(x) - find g'(a) (inverse derivatives)

1/f'(b)

d/dx sin⁻¹u

u'/√(1-u²)

d/dx cos^-1u

-u'/√(1-u²)

d/dx sec^-1u

u'/(|u|√(u²-1))

d/dx csc^-1u

-u'/(|u|√(u²-1))

d/dx tan⁻¹u

u'/(1+u²)

d/dx cot^-1u

-u'/(1+u²)

d/dx e^u

e^u * u'

d/dx a^u

a^u * u' * lna

d/dx lnu

u'/u

d/dx log_au

u'/(ulna)