## anonymous 5 years ago Find the derivatives of the following functions, and simplify into the forms specified. (a) g(x)=x3(3lnx−8). The derivative of g(x) can be expressed in the form g(x)=x2h(x), where h(x) is some function of x. Find h(x).

1. anonymous

so g'(x)=x2h(x) just want to be sure that you mean that.

2. anonymous

now $g(x)= x^3(3lnx-8)$ ???

3. anonymous

$g \prime(x) = x ^{2}h(x)$

4. anonymous

yes the second one is what i meant by that as well . sorry

5. anonymous

h(x)= 9lnx-21

6. anonymous

$g(x)= 3x^3lnx -8x^3$ $g'(x)= 3x^3(1/x) +9x^2lnx - 24x^2$ $g'(x)=3x^2+9x^2lnx-24x^2$ $x^2h(x)= 9x^2lnx-21x^2$ $h(x)= 9lnx-21$

7. anonymous

8. anonymous

let me see

9. anonymous

$y=\ln(4e^(9x)+x^6)$???

10. anonymous

yes but the 9x is to the exponent

11. anonymous

dy/dx = [ 36e^(9x) + 6x^5 ] / (4e^9x +x^6)