Derivative Rules

constant rule

d/dx(C)=0

power rule

d/dx(x^n)=nx^n-1

sum rule

d/dx(f(x)+g(x))= d/dx(f(x))+d/dx(g(x))

difference rule

d/dx(f(x)-g(x))= d/dx(f(x))-d/dx(g(x))

constant multiple rule

d/dx(cf(x)=c d/dxf(x)

product rule

d/dx(g(x)h(x)= g’(x)h(x)+g(x)h’(x)

quotient rule

d/dx (f(x)/g(x))= (f’(x)g(x)-f(x)g’(x))/(g(x))²

chain rule

d/dx(fºg)= f’(g(x))g’(x)

e rule

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

d/dx(e)or(e^c)=0

d/dx(e^cx)=ce^cx

Ln rule

d/dx(Lnx)=1/x

secant line

average rate of change

• slope of the line from x=a to x=b is msec=(f(b)-f(a))/b-a

tangent line

instantaneous rate of change

• slope at x=a is f’(a)

limit definition of derivative

(f(x+h)-f(x))/h