Question

dU In what way(s) is(are) there a difference between ax andみ? (0.25 marks) In what way(s) is(are) there similarities between dul and u7 (0.25 marks)

Answer 1

$\small \frac{\mathrm{d} U}{\mathrm{d} x } \text{ is the total derivative which measures total rate change of U w.r.t. x }$

$\small \frac{\partial U}{\partial x} \text{ is the partial derivative which measures rate change of U w.r.t. x keeping other variables constant }$

The advantage associated with taking partial derivative is the elimination of indirect dependencies between variables assumed to be constant in partial derivatives otherwise a chain rule is required to take this into effect while calculating total derivative.

The similarities between total and partial derivative is both measure the rate change of U w.r.t x.