Question

What is the derivative of `f(x) = 3^(2x)/x`?

Answer 1

`f'(x)=(3^(2x)(2xln(3)-1))/x^2`

Explanation:

We are given `f(x)=3^(2x)/x`

`f'(x)=d/dx[3^(2x)/x]`

`color(white)(f'(x))=(xd/dx[3^(2x)]-3^(2x)d/dx[x])/x^2`

`color(white)(f'(x))=(x(ln(3)*3^(2x)*d/dx[2x])-3^(2x)(1))/x^2`

`color(white)(f'(x))=(x(3^(2x)ln(3)*d/dx[2x])-3^(2x))/x^2`

`color(white)(f'(x))=(x(3^(2x)ln(3)*2)-3^(2x))/x^2`

`color(white)(f'(x))=(3^(2x)2xln(3)-3^(2x))/x^2`

`color(white)(f'(x))=(3^(2x)(2xln(3)-1))/x^2`