another derivative problem

Question

can i get thr steps to finding this please?

f(z)=4/3ln((-4x^3)+(6x^2))

Answer 1

I assume you meant to write f(x) on the left side?  

 

You need to apply the chain rule, I usually define a variable

 

u = - 4x³ +6x²

 

So you can write your function as 4/3ln(u) where u is a function of x. Ignoring the 4/3 for a moment: 

 

Apply the chain-rule

 

dy/dx = (dy/du)(du/dx)

 

dy/du = 1/u = 1/(-4x³+6x²)

 

du/dx = -12x² + 12x

 

Now put it all together: 

 

(-12x²+12x)/(-4x³+6x²) 

 

Then simplify. Don't forget to bring back the 4/3.