Question

how can we find differntial of a logrithmic function?

Answer 1

d/dx(log x)=1/x

Answer 2

but if we hve 2 take log ov a rational expression

Answer 3

Do you have an example?

Answer 4

If you have a logarithm of a rational expression, use the chain rule.

Answer 5

log3underroot 40x+90

Answer 6

\[\log _{3} \sqrt{40x+90}\] ?

Answer 7

exactly..

Answer 8

first change the base and bring the 1/2 out the front, using log rules ( http://www.themathpage.com/aPreCalc/logarithms.htm#change):
\[\log _{3} {(40x+90)^{0.5}} = 0.5 \times \frac{ \ln {(40x+90)} }{ \ln 3 }\]

Answer 9

now we differentiate it
\[\frac{ d }{dx }\frac{ 1}{ 2\ln 3 } \ln (40x+90)= \frac{ 1}{ 2\ln 3 } \times \frac{ 1 }{ 40x+90}\times 40\]

Answer 10

thanks

Answer 11

The last part is using the chain rule.
\[\frac{ d }{ dx } \ln (fx)) = \frac{ 1 }{ f(x) } \times f \prime (x)\]