Question

How do you differentiate `f(x)=log (x/5)`?

Answer 1

`\frac{d}{dx}(log_e(x/5))=1/x`

Explanation:

Given `f(x)=log_e(x/5)`

You'll surely be knowing these 2 important general equations to understand the rest. `d/dx(logx)=1/x` and `d/dxf(g(x))=f'(g(x))*g'(x)`

Now, taking the equation, we get `f'(x)=1/(x/5)*d(x/5)/dx=cancel{5}^1/x*1/cancel{5}^1=1/x`