Question

Find $d y / d x$ and $d y / d t$. $y=\frac{t}{x^2}+\frac{x}{t}$

    Find $d y / d x$ and $d y / d t$.
$y=\frac{t}{x^2}+\frac{x}{t}$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 36 ↓
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Find $d y / d x$ and $d y / d t$. $y=\frac{t}{x^2}+\frac{x}{t}$
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Transcript

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00:01 So we're asked to find dx, d, d, y, d, t, d, d, y, d x, is just going to be taking the d, d, y, d x, d equal t minus the natural log of t.
00:08 Y equals t squared minus t to negative 2.
00:15 So dx, t is just going to be taking the derivative of x with respect to t, leaving us with one minus one over t.
00:22 And let's simplify this to be, uh, t minus one over t.
00:28 Then d, y, dt, we just take the derivative of y with respect to t, and we get two t...
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