Question

Find $d y / d x$ and $d y / d t$. $y=t x^2+t^3 x$

    Find $d y / d x$ and $d y / d t$.
$y=t x^2+t^3 x$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 35 ↓
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Find $d y / d x$ and $d y / d t$. $y=t x^2+t^3 x$
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Transcript

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00:01 So let me just jot down this y equals t over x squared, and then we have plus x over t.
00:16 And i'm going to rewrite both of those.
00:18 So we have y equals t x to the negative second power plus x t to the negative first power.
00:26 Now the first thing that they asked you to do, i hope you understand that that's true because of the negative exponents.
00:34 If you move powers, you just have to change the sign of the exponent.
00:39 So the first thing they ask you to do is d -y -d -x, which means x is your independent variable.
00:44 So i -b for independent variable.
00:47 And t is a constant.
00:51 So what that means is as i do the power rule, move the exponent in front, you don't mess with the t.
00:59 You just leave it there.
01:01 And when you subtract one from negative 2, you get negative 3.
01:04 Same thing with the next one.
01:06 Move the negative 1 in front...
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