Derivative of x¹⁰+10^x+e^x

1. Differentiate $e^{x} + \left(10^{x} + x^{10}\right)$ term by term:

   1. Differentiate $10^{x} + x^{10}$ term by term:

      1. Apply the power rule: $x^{10}$ goes to $10 x^{9}$

      2. $\frac{d}{d x} 10^{x} = 10^{x} \log{\left(10 \right)}$

      The result is: $10^{x} \log{\left(10 \right)} + 10 x^{9}$

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

   The result is: $10^{x} \log{\left(10 \right)} + 10 x^{9} + e^{x}$

The answer is:

$$10^{x} \log{\left(10 \right)} + 10 x^{9} + e^{x}$$