Thread: Differentiating the real log

Find the Derivative:


the answer is
How??

Originally Posted by ^_^Engineer_Adam^_^

Find the Derivative:


the answer is
How??

You need the change of base formula for logarithms:

,

or in this case:

.

So:

.

This may be differentiated using the quotiont rule (or the product rule):



......

RonL

Originally Posted by ^_^Engineer_Adam^_^

Find the Derivative:


the answer is
How??

h(x) = Log(x) /x ------where "Log" is to the base 10.

Notes:
-----d/dx Log(base b)[u] = [1 /ln(b)]*(1/u) du/dx

-----To change log(base b)[A] to log(base c), then:
log(base b)[A] = log(base c)[A] / log(base c)[b]

So,
h'(x) = {x[(1/ln(10) *1/x] -Log(x)} /x^2
h'(x) = {1/ln(10) -Log(x)} /x^2

Convert the ln(10) to Log(10),

h'(x) = {[1 / Log(10)/Log(e)] -Log(x)} /x^2

h'(x) = {(Log(e) /Log(10)) -Log(x)} /x^2
h'(x) = {(Log(e) /1) -Log(x)} /x^2
h'(x) = {Log(e) -Log(x)} /x^2
h'(x) = Log(e/x) /x^2 ---------------answer.