The image you provided contains five calculus problems related to differentiation. Here's a breakdown of the problems:

1. Differentiate:
   $f(x) = x^3 e^x - \ln(x^2 + 1)$

2. Find $g'(x)$ if:
   $g(x) = \frac{e^x + \sin(x)}{x^2 + 1}$

3. Differentiate:
   $h(x) = \tan(x) \ln(x) + e^{x^2}$

4. Find $y'$ if:
   $y = \sin(x)^{\cos(x)}$

5. Differentiate:
   $z(x) = x^x + e^{\sin(x)} + \frac{\ln(x)}{x}$

Would you like me to walk you through the solutions step-by-step? Let me know if you need specific details for any of the problems!