Hello everyone!
i was asked to use the quotient rule to differentiate
h(x) = ( 1 + ln(x) ) / x where x > 0
I got
k'(x) = ( x + (1/x) - 1 + ln(x) * 1 ) / x^2
k'(x) = ( ln(x) ) / x^2
which i think is right.
it then asks me to use the above answer to find the general soltion of the differentisl equation
dy/dx = -(( ln(x) ) / x^2)) y^1/2 where x>0 and y>0
and give the solution in implicit form which i can't do. i am also not sure how to integrate ln(x), i find it confusing.
uote=Sweeties;146108]Hello everyone!
i was asked to use the quotient rule to differentiate
h(x) = ( 1 + ln(x) ) / x where x > 0
I got
k'(x) = ( x + (1/x) - 1 + ln(x) * 1 ) / x^2 x + (1/x) this should be x*(1/x)
according to the quotient rule
k'(x) = ( ln(x) ) / x^2 this would then change the
answer you got
which i think is right.
it then asks me to use the above answer to find the general soltion of the differentisl equation
dy/dx = -(( ln(x) ) / x^2)) y^1/2 where x>0 and y>0
and give the solution in implicit form which i can't do. i am also not sure how to integrate ln(x), i find it confusing.[/quote]