Differentiate? HELP?

Question

I'm supposed to differentiate these two problems

G(x) = Ln (x^5 - 3x^2 + 5)

and

F(x) = 3e^x / Ln(2x)

i'm lost can anyone help?

Answer 1

G(x) = Ln (x^5 - 3x^2 + 5)
G'(x) = 1/(x^5 - 3x^2 + 5) *(5x^4-6x)
and

F(x) = 3e^x / Ln(2x)
F'(x) = [ Ln(2x)*3e^x - 3e^x*1/x] / [ Ln(2x)]^2

Answer 2

d/dx (G(x)) = d/dx( ln(u)) = du/dx (1/u)
Where u = x^5 - 3x^2 + 5
And du/dx = 5x^4 - 6x

So d/dx (G(x)) = (5x^4 - 6x)/(x^5 - 3x^2 + 5)


F(x) = 3e^x / Ln(2x)
Set u = 3e^x and v = Ln(2x)

d/dx(u/v) = (v du/dx - u dv/dx)/v^2

du/dx = 3e^x and dv/dx = (d(2x)/dx)/2x = 1/x

d/dx (F(x)) = (Ln(2x) *3e^x - 3e^x*( 1/x))/(Ln(2x) *Ln(2x) )
d/dx (F(x)) = 3e^x (Ln(2x) - 1/x)/(Ln(2x) *Ln(2x) )