A particle moves along the x-axis with the velocity dx/dt= f(x). Show that the particle's acceleration is f(x)f '(x).
The notation looks funny. It usually is dy/dx. This time it's the derivative of x with respect to t.
Tried chain rule (where f is outside and x is inside), and the product rule.
"WOuldn't the derivative of f(x) just be f'(x)" This statement is only true if you derivate wrt x. Now the problem says that you have to derivate wrt t
As shilz222 pointed out you have to use the chain rule because x is a function of t, that means x isn't a single variable here but a function.