Question

How do you differentiate `f(x)=ln2^x/(3ln3x)`?

Answer 1

`f'(x)=(3ln2ln3x-3/xln2^x)/(9ln^2(3x)`.

Explanation:

I will make use of the following rules of differentiation to evaluate this:

The quotient rule : `d/dx[f(x)/g(x)]=(g(x)*f'(x)-f(x)*g'(x))/([g(x)]^2`

Log rule with power rule: `d/dx[lnu(x)]=1/u*(du)/(dx)`

Exponential rule : `d/dxa^x=a^xlna`.

`therefored/dx((ln2^x)/(3ln3x))=(((3ln3x)*1/2^x*2^xln2)-((ln2^x)*3/(3x)*3))/((3ln3x)^2)`

`=(3ln2ln3x-3/xln2^x)/(9ln^2(3x)`.