anonymous
  • anonymous
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).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
so g'(x)=x2h(x) just want to be sure that you mean that.
anonymous
  • anonymous
now \[g(x)= x^3(3lnx-8)\] ???
anonymous
  • anonymous
\[g \prime(x) = x ^{2}h(x)\]

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anonymous
  • anonymous
yes the second one is what i meant by that as well . sorry
anonymous
  • anonymous
h(x)= 9lnx-21
anonymous
  • anonymous
\[g(x)= 3x^3lnx -8x^3\] \[g'(x)= 3x^3(1/x) +9x^2lnx - 24x^2\] \[g'(x)=3x^2+9x^2lnx-24x^2\] \[x^2h(x)= 9x^2lnx-21x^2\] \[h(x)= 9lnx-21\]
anonymous
  • anonymous
thank you. could you please help me with this one as well? (b) y=ln(4e^(9x)+x^6). find dy/dx
anonymous
  • anonymous
let me see
anonymous
  • anonymous
\[y=\ln(4e^(9x)+x^6)\]???
anonymous
  • anonymous
yes but the 9x is to the exponent
anonymous
  • anonymous
dy/dx = [ 36e^(9x) + 6x^5 ] / (4e^9x +x^6)

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