Find dy/dx for y = x^3*e^x*cos(x)
In this problem, we see that y is a product of 3 functions of x. That means that in order to find dy/dx we need to use the product rule. The product rule tells us that in this case we should differentiate one function at a time, keeping the others unchanged. That would mean that we will end with 3 terms - one for each function that we differentiate - multiplied by the other 2. So the solution here will be: firstly: d(x3 )/dx= 3x2 secondly: d(ex)/dx = ex thirdly: d(cos(x))/dx = -sin(x) and so the solution is: dy/dx = 3*x2*ex*cos(x) + x3*ex*cos(x) + x3ex(-sin(x))
