find-the-differential-of-each-function-a-y-xe4x-b-y-sqrt-1-t4

Question

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

Amrita Bhasin · Accepted Answer

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&#x27;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.

Problem

Find the differential of each function. (a) $ y …

Problem 11 Medium Difficulty

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

Answer

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

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Video Transcript

Calculus: Early Transcendentals

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Calculus: Early Transcendentals

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Anna Marie V.

Kristen K.

Samuel H.

Michael J.

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