It looks like you're working with a function $z$ involving $x$ and $y$. I’ll first clarify the expression and then analyze it.

Given function:

$z = \left( x^5 \ln y + 3x^4 e^x \right) \left( 2y^5 - 7x^3 y^6 \right)$

Would you like me to differentiate $z$ with respect to $x$, $y$, or both (partial derivatives)? Or are you looking for simplification, expansion, or another type of analysis?

Related Questions:

1. How do you find the partial derivative of a product of two functions?
2. How do logarithmic and exponential functions behave under differentiation?
3. What are common techniques for simplifying polynomial-exponential expressions?
4. How does the chain rule apply to functions like $z(x, y)$?
5. How can this function be used in optimization problems?

Tip:

For differentiation of products like this, the product rule is essential:
$(uv)' = u'v + uv'$
Let me know what you need!