What are the rules of differentiation?

Answer 1

While no set of rules can handle differentiating every expression, the following should help. For all of the following, assume c and n are constants, f(x) and g(x) are functions of x, and f'(x) and g'(x) mean the derivative of f and g respectively.

Constant derivative rule:d/dx(c)=0

Constant multiple rule:d/dx(c*f(x))=c*f'(x)

Sum and Difference Rule:d/dx(f(x)±g(x))=f'(x)±g'(x)

Power rule:d/dx(xn)=n*xn-1

Product rule:d/dx(f(x)*g(x))=f'(x)*g(x) + g'(x)*f(x)

Quotient rule:d/dx(f(x)/g(x))=(f'(x)*g(x)-g'(x)*f(x))/f(x)²

Chain rule:d/dx(f(g(x))= f'(g(x))*g'(x)