Answer:
If you mean: y =(lnx)
3
then:
dy
/dx = [3(lnx)
Step-by-step explanation:
The value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
Integration is the operation which is used to find the original function from its darivative form.
The differencial function is given that
[tex]f'(x) = 6\ln x[/tex]
Integrate this function, with respect to the x,
[tex]f(x) =\int { 6\ln x} \, dx\\f(x) =6(\int { \ln x} )\, dx\\f(x) =6(x\ln x-\int { 1} \, dx)+C\\f(x) =6(x\ln x-x)+C\\f(x)=6x(\ln x-1)+C[/tex]
The value of function at 2 is,
[tex]f(2) = -3.682[/tex]
Put this value in the above equation as,
[tex]f(2)=6(2)(\ln (2)-1)+C\\-3.682=12(0.6931-1)+C\\-3.682=-3.682+C\\0=C[/tex]
Hence the value of constat is 0. Thus, the value of function at 3 is,
[tex]f(3)=6(3)(\ln (3)-1)+0\\f(3)=18(1.0986-1)\\f(3)=1.7748[/tex]
Hence, the value of the function f(3) when, given that differencial function f'(x) = 6lnx and f(2) = -3.682, is 1.7748.
Learn more about the integration of a function here;
https://brainly.com/question/17200095
