What is product rule differentiation?

Product rule differentiation, is a form of differentiation which is used to calculate the derivative, i.e. the gradient of the function, of a function f(x) which is made up of one function g(x) multiplied by another function t(x). So given f(x)= g(x).t(x) we can calculate its derivative f'(x). First we calculate the individual derivatives t'(x) and g'(x) we then calculate the derivative of the function f(x) using the formula f'(x)=t'(x)g(x)+g'(x)t(x).For example given the function f(x)=x³sin(x) so t(x)=x³ , t'(x)=3x² , g(x)=sin(x) g'(x)=cos(x) therefore f'(x)=3x²sin(x)+x³cos(x)