Derivative of 2x^4-3e^x+4lnx-5x

1. Differentiate $- 5 x + \left(\left(- 3 e^{x} + 2 x^{4}\right) + 4 \log{\left(x \right)}\right)$ term by term:

   1. Differentiate $\left(- 3 e^{x} + 2 x^{4}\right) + 4 \log{\left(x \right)}$ term by term:

      1. Differentiate $- 3 e^{x} + 2 x^{4}$ 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: $x^{4}$ goes to $4 x^{3}$

            So, the result is: $8 x^{3}$

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

            1. The derivative of $e^{x}$ is itself.

            So, the result is: $- 3 e^{x}$

         The result is: $8 x^{3} - 3 e^{x}$

      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: $8 x^{3} - 3 e^{x} + \frac{4}{x}$

   2. 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: $-5$

   The result is: $8 x^{3} - 3 e^{x} - 5 + \frac{4}{x}$

The answer is:

$$8 x^{3} - 3 e^{x} - 5 + \frac{4}{x}$$