Find the differential dy of the given function. (Use "dx" for dx.)

Question

y=x+1/4x-9

I got -13/(4x-9)^2 but it got marked wrong. Help?

Answer 1

if y(x) = x+1/(4x-9) and you want the derivative of y with respect to x:

dy/dx = d/dx(x)+ d/dx(1/(4x-9))

dy/dx = 1 + d/dx((4x-9)^-1)

Now use a variable substitution: u = 4x - 9

now d/dx(u^-1) = (du/dx)(d/du)(u^-1) (according to the chain rule)

du/dx = 4

d/du(u^-1) = -1u^-2 = -1/(4x-9)²

d/dx((4x-9)^-1) = -4/(4x-9)²

so dy/dx = 1-4/(4x-9)² (this is the answer that I would get)

Answer 2