from PIL import Image import pytesseract

Load the image to process text

image_path = "/mnt/data/1732212243521fggxq9tu.jpg" text = pytesseract.image_to_string(Image.open(image_path))

text'320. Find the equation of the tangent line to the graph of\nthe equation sin“!x+sin~!y = at the point (0, 4)\n\n321. Find the equation of the tangent line to the graph of\nthe equation tan“! (x+y) =a +h at the point (0, 1).\n\n322. Find y’ and y" for x7 + 6xy —2y?\n''320. Find the equation of the tangent line to the graph of\nthe equation sin“!x+sin~!y = at the point (0, 4)\n\n321. Find the equation of the tangent line to the graph of\nthe equation tan“! (x+y) =a +h at the point (0, 1).\n\n322. Find y’ and y" for x7 + 6xy —2y?\n'successHere is the interpretation of the text:

1. Problem 320: Find the equation of the tangent line to the graph of the equation: $\sin^{-1}(x) + \sin^{-1}(y) = \frac{\pi}{6}$ at the point $(0, \frac{1}{2})$.

2. Problem 321: Find the equation of the tangent line to the graph of the equation: $\tan^{-1}(x+y) = x^2 + \frac{\pi}{4}$ at the point $(0, 1)$.

3. Problem 322: Find $y'$ and $y''$ for: $x^2 + 6xy - 2y^2 = 3$

Now, I will solve these problems one by one.### Solution to Problem 320:

Given: $\sin^{-1}(x) + \sin^{-1}(y) = \frac{\pi}{6}$ at the point $(0, \frac{1}{2})$.

Step 1: Implicit Differentiation

Differentiating both sides with respect to $x$, we use the chain rule: [ \frac{d}{dx} \left[ \sin^{-1}(x) + \sin^{-1}(y) \right] = \frac{d}{dx} \left[ \frac{\pi}{6} \right]. ] $\frac{1}{\sqrt{1-x^2}} + \frac{1}{\sqrt{1-y^2}} \cdot \frac{dy}{dx} = 0.$ Let $y' = \frac{dy}{dx}$. Rearrange: [ \frac{1}{\sqrt{1-x^2}} + \frac{y'}{\sqrt{1-y^2}} =