
Here we compute derivatives of products and quotients of functions

### The product rule

Consider the product of two simple functions, say where $f(x)=x^2+1$ and $g(x)=x^3-3x$. An obvious guess for the derivative of $f(x)g(x)$ is the product of the derivatives:

Is this guess correct? We can check by rewriting $f$ and $g$ and doing the calculation in a way that is known to work. Write with me

Hence so we see that So the derivative of $f(x)g(x)$ is not as simple as $f'(x)g'(x)$. Never fear, we have a rule for exactly this situation.