Implicit Differentiation Question

[asset8789]

I am having trouble with a few questions. I am posting all separately to avoid any confusion. Would someone mind walking me through the following problem?

Let y be a differentiable function with (dy/dx) > 0 for all x. For which of the following values of y is it true that (d/dx)y^2 = 8(d/dx) ln y?
I. y = 1/2
II. y = 2
III. y = 4
A) I only
B) II only
C) III only
D) I and II
E) II and III

 

[blamocur]

Can you figure out both of the derivatives?

 

[asset8789]

Can you figure out both of the derivatives?

I am confused as to which things I am supposed to be taking the derivative of. Are you referring to (d/dx)y^2 = 8(d/dx) ln y?

 

[asset8789]

I am confused as to which things I am supposed to be taking the derivative of. Are you referring to (d/dx)y^2 = 8(d/dx) ln y?

Am I supposed to take both sides, like 2x = 8 (1/y)?

 

[skeeter]

Am I supposed to take both sides, like 2x = 8 (1/y)?

[imath]\dfrac{d}{dx}(y^2) = 2y \cdot \dfrac{dy}{dx}[/imath]

[imath]8 \cdot \dfrac{d}{dx} (\ln{y}) = \dfrac{8}{y} \cdot \dfrac{dy}{dx}[/imath]

now what?

 

[blamocur]

Am I supposed to take both sides, like 2x = 8 (1/y)?

Why [imath]2x[/imath]?