Question

Find $\frac{dw}{dt}$ by using the Chain Rule. Express your final answer in $w = \sqrt{x^2 + y^2 - z^2}$; $x = \cos s^2t$, $y = \sin s^2t$, $z = s^2t^2$

Name: find fracdwdt by using the chain rule express your final answer in w sqrtx2 y2 z2 x cos s2t y sin s2t z s2t2 48243
Uploaded: 2021-06-13T22:06:03-08:00
Duration: 1 min 35 s
Channel: Vikash Ranjan
Description: find fracdwdt by using the chain rule express your final answer in w sqrtx2 y2 z2 x cos s2t y sin s2t z s2t2 48243

          Find $\frac{dw}{dt}$ by using the Chain Rule. Express your final answer in
$w = \sqrt{x^2 + y^2 - z^2}$; $x = \cos s^2t$, $y = \sin s^2t$, $z = s^2t^2$

$find fracdwdt by using the chain rule express your final answer in w sqrtx2 y2 z2 x cos s2t y sin s2t z s2t2 48243$

Added by Matthew G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vikash Ranjan

06/13/2021

Step 1

The Chain Rule for $w = f(x, y, z)$ where $x, y, z$ are functions of $t$ is: $\frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{dx}{dt} + \frac{\partial w}{\partial y} \frac{dy}{dt} + \frac{\partial w}{\partial z} \frac{dz}{dt}$ First, let's find the partial Show more…

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Find $\frac{dw}{dt}$ by using the Chain Rule. Express your final answer in $w = \sqrt{x^2 + y^2 - z^2}$; $x = \cos s^2t$, $y = \sin s^2t$, $z = s^2t^2$