import Image import pytesseract

Load the uploaded image to extract the mathematical expression

image_path = "/mnt/data/1733234028534d2alkjps.jpg" text = pytesseract.image_to_string(Image.openIt seems the text extraction didn't work effectively. However, from the visible image provided, the expression looks like $-x e^y$. I will proceed to partially differentiate this expression with respect to $x$.

Partial Differentiation with respect to $x$:

The given function is $-x e^y$. Differentiating it with respect to $x$, while treating $y$ as a constant, yields:

$\frac{\partial}{\partial x}(-x e^y) = -e^y$

Would you like further clarification or an explanation of the steps?

Related Questions:

1. What does partial differentiation mean in multivariable calculus?
2. How does treating variables as constants simplify partial differentiation?
3. What is the physical significance of partial derivatives in real-world problems?
4. How would the result change if the differentiation were with respect to $y$?
5. Can partial derivatives be visualized geometrically?

Tip:

When differentiating partially, always remember which variables are held constant—it helps avoid unnecessary errors.