💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the differential of each function.(a) $ y = xe^{4x} $(b) $ y = \sqrt {1 -t^4} $

(a) $(1-4 x) e^{-4 x} d x$(b) $d y=-\frac{2 t^{3}}{\sqrt{1-t^{4}}} d t$

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:49

Find the differential of e…

01:27

02:51

Find the differential of t…

01:09

03:06

Solve the given differenti…

02:04

Find the differential $d y…

01:25

Solve the differential equ…

01:30

Verify that the given func…

05:59

04:07

Show that each function $y…

okay. Part A The derivative using the product rule. We have acts times You did the negative for ox Natural order of E. We know that we're taking the derivative of negative four acts. So in this case, this simplifies to negative for X E to the negative or ax plus e to the night of four ax using the chain rule and factoring we end up with Okay, Part B. We know that we have one nice t to the fourth to the 1/2. Therefore we have, if you have tea, is one nice to the fourth than we know that we could have 1/2 you to the negative. 1/2 comes negative for t cubed, which is negative to t cubed over the square root of one minus t to the fourth.

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find the differential of each function.(a) $ y = \tan \sqrt t $(b) $…

Find the differential of each function.$$(a) y=\tan \sqrt{t}$$$$(b) …

Find the differential of the function.$ u = \sqrt{x^2 + 3y^2} $

Find the differential of the function.$$u=\sqrt{x^{2}+3 y^{2}}$$…

Solve the given differential equation.$$y^{\prime \prime}=2 x^{-1} y^{\p…

Find the differential $d y$$$\text { (a) } y=x \sqrt{1-x} \quad \tex…

Solve the differential equation.$$\frac { d y } { d t } = \frac { t e ^ …

Verify that the given function is a solution of the differential equation.

Solve the given differential equation.$$y^{\prime}-x^{-1} y=4 x^{2} y^{-…

Show that each function $y=f(x)$ is a solution of the accompanying different…