Question

find the derivative: 3lnx/x^2

Answer 1

applying quotient rule as follows

Answer 2

\[d/dx(3lnx/x^2)\]

Answer 3

{[3x]-6xlnx}/x^{4}

Answer 4

hmmmm I don't know if that's right nor not :)

Answer 5

d1st(2nd) -d2nd(1st)/2nd^2 is the formula right?

Answer 6

yes but denominator has whole square of function in denominator

Answer 7

i am writing in detail just a sec

Answer 8

d/d((f(x))/g(x) =(f^' (x)g(x)-f(x) g^' (x))/〖{g(x)}〗^2

Answer 9

what is meant by the word differentiable and to differentiate?

Answer 10

[3x-6xlnx]/x^4
taking 3x common and cancelling x
finally
3[1-6lnx]/x^3

Answer 11

differentiate means finding derivative simply by applying formulae already known and differentiable function means a function who's right derivative and left derivative exist

Answer 12

In calculus (a branch of mathematics), a differentiable function is a function whose derivative exists at each point in its domain.

Answer 13

a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.

Answer 14

ok but what I don't follow here is two things 1) how you handled the numerator and 2) how you ended up with x^3 in the denominator

Answer 15

let us denote numerator by f(x) and denominator by g(x)
then in numerator we have g(x)f'(x)-f(x)g'(x)
where f'(x) and g'(x) means their derivatives
in denominator we have [g(x)]^2
right this is the quotient rule, if u get it remaining is too easy

Answer 16

i am finding difficulty in typing fractions here

Answer 17

I get it but I still don't get how to find the derivative of 3lnx

Answer 18

f(x)=3lnx so f'(x)=3/x because derivative of lnx is 1/x

Answer 19

the quotient rule I get but I don't get how to find the derivative of a natural log or a regular log for that matter

Answer 20

and g(x)=x^2 so derivative g'(x)=2x
by power rule

Answer 21

putting the values and simplifying u get the answer

Answer 22

ok I think I remember lnx=1/x, so 3lnx=3/x?

Answer 23

yes

Answer 24

I still don't see how you got 3(1-6lnx) in the numerator if the derivative of the numerator is 3/x

Answer 25

in numerator putting values we get numerator as
3(x^2)x-(3lnx)(2x)
=3x-6xlnx
=3x(1-2lnx)
sorry i wrote 6 earlier:D
then cancel this x of numerator with one of x in denominator

Answer 26

ok I worked it on paper and I got.....