from PIL import Image import pytesseract

Load the image to extract text

image_path = "/mnt/data/1732427589632rn91ep24.jpg" extracted_text = pytesseract.image_to_string(Image.open(image_path), lang='eng')

extracted_text'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'successBased on the extracted text, I will solve the derivatives of the given functions step by step.

Given:

1. $y = 3x^4 + x^3$
2. $y = \pi x^7 - 2x^5 - 5x^{-2}$
3. $y = (x^2 + 17)(x^3 - 3x + 1)$
4. $y = \frac{5x^2 + 2x - 6}{3x - 1}$

1. $y = 3x^4 + x^3$

The derivative: $f'(x) = \frac{d}{dx}(3x^4) + \frac{d}{dx}(x^3) = 12x^3 + 3x^2$

2. $y = \pi x^7 - 2x^5 - 5x^{-2}$

The derivative: $f'(x) = \frac{d}{dx}(\pi x^7) - \frac{d}{dx}(2x^5) - \frac{d}{dx}(5x^{-2})$ $f'(x) = 7\pi x^6 - 10x^4 + 10x^{-3}$

3. $y = (x^2 + 17)(x^3 - 3x + 1)$

Using the product rule: $f'(x) = \frac{d}{dx}(x^2 + 17) \cdot (x^3 - 3x + 1) + (x^2 + 17) \cdot \frac{d}{dx}(x^3 - 3x + 1)$ $f'(x) = (2x)(x^3 - 3x + 1) + (x^2 + 17)(3x^2 - 3)$ Simplify: $f'(x) = 2x^4 - 6x^2 + 2x + 3x^4 - 3x^2 + 51x^2 - 51$ $f'(x) = 5x^4 + 42x^2 + 2x - 51$

4. $y = \frac{5x^2 + 2x - 6}{3x - 1}$

Using the quotient rule: $f'(x) = \frac{(3x - 1) \cdot \frac{d}{dx}(5x^2 + 2x - 6) - (5x^2 + 2x - 6) \cdot \frac{d}{dx}(3x - 1)}{(3x - 1)^2}$ $f'(x) = \frac{(3x - 1)(10x + 2) - (5x^2 + 2x - 6)(3)}{(3x - 1)^2}$ Simplify: $f'(x) = \frac{30x^2 + 6x - 10x - 2 - 15x^2 - 6x + 18}{(3x - 1)^2}$ $f'(x) = \frac{15x^2 - 12}{(3x - 1)^2}$

If you'd like, I can elaborate on these calculations or tackle any additional questions.

5 Related Questions:

1. How do we apply the product rule in derivative calculations?
2. How does the chain rule differ from the product rule?
3. Can you explain when to use the quotient rule in differentiation?
4. How do constants like $\pi$ affect derivatives?
5. What are some common mistakes when simplifying derivatives?

Tip:

Always simplify the expressions after applying derivative rules to avoid errors and make the answer clearer.