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).

Question

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).

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

h(x)= 9lnx-21

anonymous · Answer

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

anonymous · Answer

thank you. could you please help me with this one as well?
(b) y=ln(4e^(9x)+x^6). find dy/dx

anonymous · Answer

let me see

anonymous · Answer

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

anonymous · Answer

yes but the 9x is to the exponent

anonymous · Answer

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