690 452 Meaning - Google Search
The number 690452 has gained popularity on TikTok, where it is said that writing it on your wrist before sleeping can trap you in a dream or parallel universe, leading to real-life consequences if you die in your sleep. This phenomenon is often referred to as a 'cursed number' and has sparked various discussions and videos exploring its meaning and implications. The trend raises questions about its authenticity and the effects it may have on individuals who engage with it.
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★(𝙵𝚄𝙻𝙻√𝚅𝙸𝙳𝙴𝙾𝚂*) Pakistani TikTok Star Minahil Malik Viral Video at Columbia Club of Atlanta
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690 452 Meaning - Google Search
The number 690452 has gained popularity on TikTok, where it is said that writing it on your wrist before sleeping can trap you in a dream or parallel universe, leading to real-life consequences if you die in your sleep. This phenomenon is often referred to as a 'cursed number' and has sparked various discussions and videos exploring its meaning and implications. The trend raises questions about its authenticity and the effects it may have on individuals who engage with it.
If y(x) = x^x , x gt 0 then y"(2) – 2y'(2) is equal to
<p>To solve the problem, we need to find <span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.082em; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′′</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.446em;">−</span></span><span class="mjx-mn MJXc-space2"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-msup"><span class="mjx-base" style="margin-right: -0.006em;"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0.082em; padding-right: 0.071em;"><span class="mjx-mo" style=""><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.298em; padding-bottom: 0.298em;">′</span></span></span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.372em; padding-bottom: 0.372em;">2</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span></span></span></span> for the function <span class="mjx-chtml MJXc-display" style="text-align: center;"><span class="mjx-math"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.519em; padding-right: 0.006em;">y</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">(</span></span><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.446em; padding-bottom: 0.593em;">)</span></span><span class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R" style="padding-top: 0.077em; padding-bottom: 0.298em;">=</span></span><span class="mjx-msubsup MJXc-space3"><span class="mjx-base"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span><span class="mjx-sup" style="font-size: 70.7%; vertical-align: 0.584em; padding-left: 0px; padding-right: 0.071em;"><span class="mjx-mi" style=""><span class="mjx-char MJXc-TeX-math-I" style="padding-top: 0.225em; padding-bottom: 0.298em;">x</span></span></span></span></span></span></span>.</p><p><strong>Step 1: Find \( y'(x) \)</strong></p><p>We start by differentiating \( y(x) = x^x \). To do this, we can use logarithmic differentiation.</p><p>1. Take the natural logarithm of both sides:
\(
\ln y = \ln(x^x) = x \ln x
\)</p><p>2. Differentiate both sides with respect to \( x \):
\(
\frac{1}{y} \frac{dy}{dx} = \ln x + 1
\)</p><p>3. Multiply through by \( y \):
\(
y' = y(\ln x + 1) = x^x(\ln x + 1)
\)</p><p><strong>Step 2: Find \( y'(2) \)</strong></p><p>Now we substitute \( x = 2 \):
\(
y'(2) = 2^2(\ln 2 + 1) = 4(\ln 2 + 1)
\)</p><p><strong>Step 3: Find \( y''(x) \)</strong></p><p>Next, we differentiate \( y'(x) \) to find \( y''(x) \). We will use the product rule:
\(
y' = x^x(\ln x + 1)
\)</p><p>Using the product rule:
\(
y'' = \frac{d}{dx}(x^x) \cdot (\ln x + 1) + x^x \cdot \frac{d}{dx}(\ln x + 1)
\)</p><p>We already found \( \frac{d}{dx}(x^x) = x^x(\ln x + 1) \), and:
\(
\frac{d}{dx}(\ln x + 1) = \frac{1}{x}
\)</p><p>Thus:
\(
y'' = x^x(\ln x + 1)(\ln x + 1) + x^x \cdot \frac{1}{x}
\)
\(
= x^x(\ln x + 1)^2 + x^{x-1}
\)</p><p><strong>Step 4: Find \( y''(2) \)</strong></p><p>Now we substitute \( x = 2 \):
\(
y''(2) = 2^2(\ln 2 + 1)^2 + 2^{2-1} = 4(\ln 2 + 1)^2 + 2
\)</p><p><strong>Step 5: Calculate \( y''(2) - 2y'(2) \)</strong></p><p>Now we can calculate:
\(
y''(2) - 2y'(2) = (4(\ln 2 + 1)^2 + 2) - 2(4(\ln 2 + 1))
\)
\(
= 4(\ln 2 + 1)^2 + 2 - 8(\ln 2 + 1)
\)</p><p><strong>Step 6: Simplify the expression</strong></p><p>Let’s simplify:
\(
= 4(\ln 2 + 1)^2 - 8(\ln 2 + 1) + 2
\)</p><p>This is a quadratic in terms of \( \ln 2 + 1 \):
Let \( u = \ln 2 + 1 \):
\(
= 4u^2 - 8u + 2
\)</p><p><strong>Step 7: Factor or use the quadratic formula</strong></p><p>We can use the quadratic formula:
\(
= 4(u^2 - 2u + \frac{1}{2}) = 4\left((u - 1)^2 - \frac{1}{2}\right)
\)</p><p><strong>Final Result</strong></p><p>Thus, the final answer is:
\(
y''(2) - 2y'(2) = 4\left((\ln 2 + 1 - 1)^2 - \frac{1}{2}\right) = 4\left((\ln 2)^2 - \frac{1}{2}\right)
\)</p>
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What does 690452 mean? The TikTok trend explained
Here's the meaning behind the 690452 trend on TikTok.
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690 452 Meaning - Google Search
The number 690452 has gained popularity on TikTok, where it is said that writing it on your wrist before sleeping can trap you in a dream or parallel universe, leading to real-life consequences if you die in your sleep. This phenomenon is often referred to as a 'cursed number' and has sparked various discussions and videos exploring its meaning and implications. The trend raises questions about its authenticity and the effects it may have on individuals who engage with it.
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