SOLUTION: I need the derivative of : y = 1 / log x The answer is supposed to be y' = -ln 10 / x(ln x) ^2 I want to know how to do this. Is there a solver on algebra.com to do this?

Algebra ->  Linear-equations -> SOLUTION: I need the derivative of : y = 1 / log x The answer is supposed to be y' = -ln 10 / x(ln x) ^2 I want to know how to do this. Is there a solver on algebra.com to do this?      Log On


   

Question 550906: I need the derivative of : y = 1 / log x
The answer is supposed to be y' = -ln 10 / x(ln x) ^2
I want to know how to do this.
Is there a solver on algebra.com to do this?
Thank you
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
y = 1%2Flog%28%28x%29%29

Use the change of base formula:

Y = 1%2F%28ln%28x%29%2Fln%2810%29%29

Write as a division:

y = 1÷ln%28x%29%2Fln%2810%29

Invert and multiply:

y = 1·ln%2810%29%2Fln%28x%29

y = ln%2810%29%2Fln%28x%29

Bring the denominator to the numerator with a -1 power 

y = ln(10)·[ln(x)]-1

                       Now we need two formulas 

                       1) expr%28d%2Fdx%29%28u%5En%29 = n%2Au%5E%28n-1%29expr%28%28du%29%2F%28dx%29%29

                       and

                       2) expr%28d%2Fdx%29ln%28u%29 = 1%2Fu·%28du%29%2F%28dx%29

y = ln(10)·[ln(x)]-1

dy%2Fdx = -1·ln(10)·[ln(x)]-2%281%2Fx%29
dy%2Fdx = -ln(10)·1%2F%28%22ln_x%22%29%5E2%281%2Fx%29
dy%2Fdx = -ln%2810%29%2F%28x%2A%28%22ln_x%22%29%5E2%29

Edwin