The product rule is the method used to differentiate the product of two functions, that's two functions being multiplied by one another.
For instance, if we were given the function defined as:
this is the product of two functions, which we typically refer to as \(u(x)\) and \(v(x)\).
So, in the case of \(f(x)=x^2sin(x)\), we would define \(u(x)=x^2\) and \(v(x)=sin(x)\), to write: \[f(x)=u(x)\times v(x)\]
In the following tutorial we review the product rule and learn how to use it with some examples.
Consider the curve defined by \(y=2x.ln(x)\).