Question

How do you find the derivative of `y = 9 ln(4 ln x)`?

Answer 1

Apply the chain rule.

Explanation:

Begin with the derivative of the outermost function, `ln`. We know that the derivative of the natural log is just one over the argument of the function. In this case, the argument is `4ln(x)`, so we begin with `1/(4ln(x))`. Of course `9` is a constant, so we leave it alone.

`=>y'=9*1/(4ln(x))*"..."`

Now we multiply by the derivative of the next function, which is `4ln(x)`. Again, we know that this derivative is just `4*1/x`

`=>y'=9*1/(4ln(x))*4*1/x*"..."`

Finally, the innermost term is just `x`, which has derivative 1.

`=>y'=9*1/(4ln(x))*4*1/x*1`

`:.y'=9/(xln(x))`