Find dy/du, du/dx, and dy/dx when y and u are defined as follows.

Question

Answer 1

dy/du = -7/u²

du/dx = 1/(2√x)

dy/dx = dy/du du/dx = (-7/u²)(1/(2√x)) = -7/(2√x u²)

u² = (√x + 7)² = x+14√x +49

dy/dx = -7/(2√x (x+14x+49))

You can get the same answer using the quotient rule of:

y = 7/u = 7/(√x + 7)