Differentiate f(x) = 14*(x^2)*(e^(x^2))

Differentiate f(x) = 14x²e^{x^2}To approach this problem we first need to realise that f(x) is made up of two simpler functions multiplied together. This tells us that we should use the product rule to solve this (if f(x) = u(x)v(x) then f'(x) = u(x)v'(x) + u'(x)v(x)) Let's say our u(x) is 14x². Then our u'(x) = 2 * 14 * x^2-1 = 28xTherefore our v(x) is e^{x^2}. If we are new to this we could then use the chain rule to solve for v'(x) OR if we are familiar with this form we might see straight away that v'(x) = 2xe^{x^2} . To get our final answer we just follow the product rule definition as above, using the solutions u'(x) and v'(x) that we've just found.