It seems that you've uploaded an image. Let me analyze the content and extract the relevant mathematical information to assist you. PIL import Image

Load and display the image to analyze its content

image_path = '/mnt/data/1733612935326n1clacav.jpg' img = Image.open(image_path) img.show()I have displayed the image for review. Let me now process and extract any mathematical information it contains. I'll get back to you with the analysis shortly. pytesseract

Use Tesseract to extract text from the image

text = pytesseract.image_to_string(img)

textThe image contains two math problems related to finding slopes of tangent lines and derivatives. Here are the extracted problems:

1. Find the slope of the line tangent to the curve $x^2 + xy + y^2 = 5$ at the point $(-1, 2)$.
2. Find $\frac{dy}{dx}$ if $x^2y + y^2x = -2$.

Would you like me to go through the solution for these problems in detail? Let me know if you'd like a step-by-step explanation.

If you're interested, here are 5 related questions that could expand your knowledge:

1. What is implicit differentiation and how does it apply to these problems?
2. How do you differentiate implicitly when both $x$ and $y$ are variables?
3. How do you find the slope of a tangent line from a derivative?
4. What is the concept of a "partial derivative" and how does it differ from an ordinary derivative?
5. How would the slope change if the point given in the problem were different?

Tip: When differentiating implicitly, always remember to apply the chain rule to terms involving $y$, as $y$ is considered a function of $x$.