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Lemon Party Là Gì? Cú troll đen tối hơn 20 năm đang tái xuất | Terrariumvibe

Khi lần đầu nghe đến cụm từ Lemon Party, bạn có tưởng tượng đây là một cộng đồng yêu thích trồng chanh hoặc một sự kiện sinh thái xanh? Thực tế, có rất nhiều

05:26 02/07/2025

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05:29 02/07/2025

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05:31 02/07/2025

CONFIRMED lineups: Barcelona vs Real Madrid, 2025 El Clasico

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05:35 02/07/2025

If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

To solve the problem, we need to find y′′(2)−2y′(2) for the function y(x)=xx.Step 1: Find \( y'(x) \)We start by differentiating \( y(x) = x^x \). To do this, we can use logarithmic differentiation.1. Take the natural logarithm of both sides: \( \ln y = \ln(x^x) = x \ln x \)2. Differentiate both sides with respect to \( x \): \( \frac{1}{y} \frac{dy}{dx} = \ln x + 1 \)3. Multiply through by \( y \): \( y' = y(\ln x + 1) = x^x(\ln x + 1) \)Step 2: Find \( y'(2) \)Now we substitute \( x = 2 \): \( y'(2) = 2^2(\ln 2 + 1) = 4(\ln 2 + 1) \)Step 3: Find \( y''(x) \)Next, we differentiate \( y'(x) \) to find \( y''(x) \). We will use the product rule: \( y' = x^x(\ln x + 1) \)Using the product rule: \( y'' = \frac{d}{dx}(x^x) \cdot (\ln x + 1) + x^x \cdot \frac{d}{dx}(\ln x + 1) \)We already found \( \frac{d}{dx}(x^x) = x^x(\ln x + 1) \), and: \( \frac{d}{dx}(\ln x + 1) = \frac{1}{x} \)Thus: \( y'' = x^x(\ln x + 1)(\ln x + 1) + x^x \cdot \frac{1}{x} \) \( = x^x(\ln x + 1)^2 + x^{x-1} \)Step 4: Find \( y''(2) \)Now we substitute \( x = 2 \): \( y''(2) = 2^2(\ln 2 + 1)^2 + 2^{2-1} = 4(\ln 2 + 1)^2 + 2 \)Step 5: Calculate \( y''(2) - 2y'(2) \)Now we can calculate: \( y''(2) - 2y'(2) = (4(\ln 2 + 1)^2 + 2) - 2(4(\ln 2 + 1)) \) \( = 4(\ln 2 + 1)^2 + 2 - 8(\ln 2 + 1) \)Step 6: Simplify the expressionLet’s simplify: \( = 4(\ln 2 + 1)^2 - 8(\ln 2 + 1) + 2 \)This is a quadratic in terms of \( \ln 2 + 1 \): Let \( u = \ln 2 + 1 \): \( = 4u^2 - 8u + 2 \)Step 7: Factor or use the quadratic formulaWe can use the quadratic formula: \( = 4(u^2 - 2u + \frac{1}{2}) = 4\left((u - 1)^2 - \frac{1}{2}\right) \)Final ResultThus, the final answer is: \( y''(2) - 2y'(2) = 4\left((\ln 2 + 1 - 1)^2 - \frac{1}{2}\right) = 4\left((\ln 2)^2 - \frac{1}{2}\right) \)

05:38 02/07/2025

Lịch sử đối đầu MU vs Crystal Palace: Tỷ số đậm

MU vs Crystal Palace không phải là hai đội bóng có sự kình địch lớn tại Premier League, nhưng mỗi lần chạm trán giữa họ đều mang đến những diễn biến đáng chú ý.

05:41 02/07/2025

★(𝙵𝚄𝙻𝙻√𝚅𝙸𝙳𝙴𝙾𝚂*) Pakistani TikTok Star Minahil Malik Viral Video at Columbia Club of Atlanta

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05:42 02/07/2025

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05:44 02/07/2025

If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

To solve the problem, we need to find y′′(2)−2y′(2) for the function y(x)=xx.Step 1: Find \( y'(x) \)We start by differentiating \( y(x) = x^x \). To do this, we can use logarithmic differentiation.1. Take the natural logarithm of both sides: \( \ln y = \ln(x^x) = x \ln x \)2. Differentiate both sides with respect to \( x \): \( \frac{1}{y} \frac{dy}{dx} = \ln x + 1 \)3. Multiply through by \( y \): \( y' = y(\ln x + 1) = x^x(\ln x + 1) \)Step 2: Find \( y'(2) \)Now we substitute \( x = 2 \): \( y'(2) = 2^2(\ln 2 + 1) = 4(\ln 2 + 1) \)Step 3: Find \( y''(x) \)Next, we differentiate \( y'(x) \) to find \( y''(x) \). We will use the product rule: \( y' = x^x(\ln x + 1) \)Using the product rule: \( y'' = \frac{d}{dx}(x^x) \cdot (\ln x + 1) + x^x \cdot \frac{d}{dx}(\ln x + 1) \)We already found \( \frac{d}{dx}(x^x) = x^x(\ln x + 1) \), and: \( \frac{d}{dx}(\ln x + 1) = \frac{1}{x} \)Thus: \( y'' = x^x(\ln x + 1)(\ln x + 1) + x^x \cdot \frac{1}{x} \) \( = x^x(\ln x + 1)^2 + x^{x-1} \)Step 4: Find \( y''(2) \)Now we substitute \( x = 2 \): \( y''(2) = 2^2(\ln 2 + 1)^2 + 2^{2-1} = 4(\ln 2 + 1)^2 + 2 \)Step 5: Calculate \( y''(2) - 2y'(2) \)Now we can calculate: \( y''(2) - 2y'(2) = (4(\ln 2 + 1)^2 + 2) - 2(4(\ln 2 + 1)) \) \( = 4(\ln 2 + 1)^2 + 2 - 8(\ln 2 + 1) \)Step 6: Simplify the expressionLet’s simplify: \( = 4(\ln 2 + 1)^2 - 8(\ln 2 + 1) + 2 \)This is a quadratic in terms of \( \ln 2 + 1 \): Let \( u = \ln 2 + 1 \): \( = 4u^2 - 8u + 2 \)Step 7: Factor or use the quadratic formulaWe can use the quadratic formula: \( = 4(u^2 - 2u + \frac{1}{2}) = 4\left((u - 1)^2 - \frac{1}{2}\right) \)Final ResultThus, the final answer is: \( y''(2) - 2y'(2) = 4\left((\ln 2 + 1 - 1)^2 - \frac{1}{2}\right) = 4\left((\ln 2)^2 - \frac{1}{2}\right) \)

05:49 02/07/2025

If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

Lemon Party Là Gì? Cú troll đen tối hơn 20 năm đang tái xuất | Terrariumvibe

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Download Blurry Black Aesthetic Mirror Selfie Picture | Wallpapers.com

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CONFIRMED lineups: Barcelona vs Real Madrid, 2025 El Clasico

If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

Lịch sử đối đầu MU vs Crystal Palace: Tỷ số đậm

★(𝙵𝚄𝙻𝙻√𝚅𝙸𝙳𝙴𝙾𝚂*) Pakistani TikTok Star Minahil Malik Viral Video at Columbia Club of Atlanta

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If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to

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