Derivative of y(x)=3x-4ln(x)-5

1. Differentiate $\left(3 x - 4 \log{\left(x \right)}\right) - 5$ term by term:

   1. Differentiate $3 x - 4 \log{\left(x \right)}$ term by term:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $3$

      2. The derivative of a constant times a function is the constant times the derivative of the function.

         1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$.

         So, the result is: $- \frac{4}{x}$

      The result is: $3 - \frac{4}{x}$

   2. The derivative of the constant $-5$ is zero.

   The result is: $3 - \frac{4}{x}$

The answer is:

$$3 - \frac{4}{x}$$