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

1 Answer
Feb 6, 2016

\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