How to Differentiate ln(x) = yln(a)

[jsmith613]

Homework Statement

Given that ln(x) = y ln(a)
find
dy/dx

Homework Equations

The Attempt at a Solution

So
y = ln(x) / ln(a)
thus we use the quotient rule
ln(x) --> 1/x
ln(a) --> 1/a

Denominator = [ln(a)]²

So the differentiated equation is

ln(a)/x - ln(x)/a
-------------------
[ln(a)]²

How would I continue this
The answer is
d/dx = 1/(x ln(a))

 

[vela]

When you differentiate, you differentiate with respect to some variable, in this case, x. Here the quantity a is a constant. Try redoing your calculation with that in mind.

 

[jsmith613]

d/dx of ln(x) / ln(a)
d/dx of ln(x) * 1/ln(a)
LETS SAY 1/ln(a) = k
thus
d/dx of k ln(x) equals
k/x
this is the same as
1/xln(a)
right?

 

[vela]

Yup!