from PIL import Image import pytesseract

Load the image to process it

image_path = '/mnt/data/1732374422358vxbrdzxf.jpg' text_from_image = pytesseract.image_to_string(Image.open(image_path), lang='eng')

text_from_image'Tugas 6\nFRSO01 - Kalkulus |\n\n1. Tentukan f(y) dari:\n\na.y =3x44+x3\n\nd.y = (x? + 17)(x3 — 3x41)\n\nb. mx? — 2x5 — 5x7?\n\ne.\n\nSx242x-6\n3x-1\n\n''Tugas 6\nFRSO01 - Kalkulus |\n\n1. Tentukan f(y) dari:\n\na.y =3x44+x3\n\nd.y = (x? + 17)(x3 — 3x41)\n\nb. mx? — 2x5 — 5x7?\n\ne.\n\nSx242x-6\n3x-1\n\n'successThe text extracted from the image appears as follows:

Tugas 6
FRS001 - Kalkulus I

1. Tentukan $f'(y)$ dari:

a. $y = 3x^4 + x^3$
b. $y = \pi x^7 - 2x^5 - 5x^{-2}$
c. $y = \frac{3}{x^3} + x^{-4}$
d. $y = (x^2 + 17)(x^3 - 3x + 1)$
e. $y = \frac{5x^2 + 2x - 6}{3x - 1}$
f. $y = \frac{2}{3x} - \frac{2}{3}$

Let me compute the derivatives $f'(y)$ for all the given functions.from sympy import symbols, diff, pi

Define the variable

x = symbols('x')

Define each function and compute its derivative

functions = { "a": 3x4 + x3, "b": pix7 - 2*x5 - 5x**(-2), "c": 3/x3 + x(-4), "d": (x2 + 17) * (x3 - 3x + 1), "e": (5x**2 + 2x - 6) / (3x - 1), "f": (2 / (3x)) - (2 / 3), }

Calculate derivatives

derivatives = {key: diff(func, x) for key, func in functions.items()}

derivatives{'a': 12x**3 + 3x2, 'b': 7pix6 - 10x4 + 10/x3, 'c': -9/x4 - 4/x5, 'd': 2x*(x3 - 3*x + 1) + (x2 + 17)(3x2 - 3), 'e': (10x + 2)/(3x - 1) - 3*(5*x2 + 2x - 6)/(3x - 1)2, 'f': -2/(3*x2)}{'a': 12x**3 + 3x2, 'b': 7pix6 - 10x4 + 10/x3, 'c': -9/x4 - 4/x5, 'd': 2x*(x3 - 3*x + 1) + (x2 + 17)(3x2 - 3), 'e': (10x + 2)/(3x - 1) - 3*(5*x2 + 2x - 6)/(3x - 1)2, 'f': -2/(3*x2)}successHere are the derivatives $f'(y)$ for the given functions:

a. $y = 3x^4 + x^3$:
$f'(y) = 12x^3 + 3x^2$

b. $y = \pi x^7 - 2x^5 - 5x^{-2}$:
$f'(y) = 7\pi x^6 - 10x^4 + \frac{10}{x^3}$

c. $y = \frac{3}{x^3} + x^{-4}$:
$f'(y) = -\frac{9}{x^4} - \frac{4}{x^5}$

d. $y = (x^2 + 17)(x^3 - 3x + 1)$:
$f'(y) = 2x(x^3 - 3x + 1) + (x^2 + 17)(3x^2 - 3)$

e. $y = \frac{5x^2 + 2x - 6}{3x - 1}$:
$f'(y) = \frac{10x + 2}{3x - 1} - \frac{3(5x^2 + 2x - 6)}{(3x - 1)^2}$

f. $y = \frac{2}{3x} - \frac{2}{3}$:
$f'(y) = -\frac{2}{3x^2}$

Let me know if you'd like detailed simplifications or further explanations for any of these steps!

Here are some related questions to expand your understanding:

1. How is the product rule applied in problem (d)?
2. What is the significance of negative exponents in problem (c)?
3. How can the quotient rule be used for rational functions like in problem (e)?
4. What happens to the derivative of a constant term, like $-\frac{2}{3}$ in problem (f)?
5. How does the chain rule apply to functions involving nested powers?

Tip: Always double-check your algebraic simplifications when applying differentiation rules, especially for product and quotient rules.