Differentiate `(log)_(10)x+(log)_x 10+(log)_(x) x+(log)_(10)10` with respect to `x` .

Explanation

Given that,

`y=(log)_(10)x+(log)_x 10+(log)_(x) x+(log)_(10)10`

`y=(log)_(10) e * (log)_(e) x+ frac{(log)_(e) 10}{(log)_(e) x}+1+1`

Differentiating w.r.t. `x` both sides

`frac{dy}{dx}=(log)_(10) e * frac{1}{x}- frac{(log)_(e) 10}{x((log)_(e) x)^2}+0+0`

`frac{dy}{dx}=frac{1}{x((log)_(e)10 )}- frac{(log)_(e) 10}{x((log)_(e) x)^2}`


Answer is:

`frac{dy}{dx}=frac{1}{x((log)_(e)10 )}- frac{(log)_(e) 10}{x((log)_(e) x)^2}`