what is the derivative of log(x)????

Answer 1

If y = ln(x), then y' = 1/x. However, you do not have ln(x), you have log(x) which is base 10, not base e.

y = log(x) implies 10^y = x. (by definition)

ln(10^y) = ln(x)

y*ln(10) = ln(x) <---- By properties of log's

y = ln(x)/ln(10) <---- Divided both sides by ln(10)

y = (1/ln(10))*ln(x) <----Rewrote as constant times ln(x)

y' = 0*ln(x) + 1/x*(1/ln(10)) <----Product Rule of Diff.

y' = 1/(x*ln(10)) <---- Simplified algebraically

This formula is usually given in calculus texts. But, as you can see, rewriting your original equation in exponential form and then applying logarithmic differentiation, the formula is readily derived. To make math and math-related classes easier, learn how to derive the formulas and STOP MEMORIZING them. Now, go finish your linearization problem for log(x) at x = 2.

Answer 2

Well, the derivative of log(x) is 1/x only when the base of that logarithm is e. (You know, Euler's number, e= 2.7182818.......).

If it's just log(x) base 10, then the derivative is 1 / (x.ln(10)), where "ln" means "log" but with a base of e.

Answer 3

actually, the derivative of ln x = 1/x. The derivative of log x is 1/ (x ln a).

Answer 4

1/xdx

Answer 5

1/x
No dx should be included