derivative ind product \( y=\left(7 x^{4}-3 x\right)\left(x^{0}+2 x^{3}\right. \) \( =\left(7 x^{4}-3 x\right) \quad v=\left(x^{0}+2 x^{3}\right) \)

To find the derivative of the product \( y = (7x^{4} - 3x)(x^{0} + 2x^{3}) \), you can apply the product rule, which states that if you have two functions \( u \) and \( v \), then the derivative is given by \( y' = u'v + uv' \). Here, \( u = (7x^{4} - 3x) \) and \( v = (x^{0} + 2x^{3}) \). First, compute the derivatives \( u' \) and \( v' \) separately, then combine them. Notably, the product rule can sometimes lead to common mistakes, such as forgetting to derive both functions or misapplying the rule. A fun tip is to visualize derivatives as if you're finding the velocity when two race cars (the functions) accelerate into a turn. Each car influences the motion, and you must account for both to find the total speed leaving the corner!