Suppose y=r²x-rx³+5r . g is the SAME as the the derivative of y with respect to r. Find dg/dx

Answer 1

To find dg/dx, we need to differentiate g with respect to x. In order to do this, we can first differentiate y with respect to r, and then differentiate the resulting expression with respect to x.

Differentiating y with respect to r using the power rule gives:
dy/dr = 2rx - 3rx² + 5

Now we can differentiate dy/dr with respect to x:
(d²y/dr²)(dr/dx) = 2r - 6rx

Since g is the same as dy/dr, we can substitute it into the expression above:
dg/dx = 2r - 6rx

So, dg/dx = 2r - 6rx.