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

Stuck on your homework problem? This step-by-step video should help.

Try Numerade Free for 30 Days

Like

Report

Find the derivatives of the given functions.$$y=4 e^{t}\left(e^{2 t}-e^{t}\right)$$

$\frac{d y}{d t}=12 e^{3 t}-8 c^{2 t}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

Campbell University

Baylor University

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

05:04

Find the derivatives of th…

02:14

Find the derivative of the…

00:56

Find derivatives of the fu…

03:07

Derivatives Find and simpl…

00:32

01:07

03:49

02:46

00:54

08:01

Uh huh. We want to find Dy DT for the function Y equals for each of the tee times either to t minus E to the T. We're gonna rely on derivative shortcuts to solve this. Specifically, rule 0 to 3. Here we're rule Zero states GDX BTU is B D u L n B D u d x G D X. Either the U. Is either the U d u d X rules one through three. Other powerful product rule in general, respectively. Before we use any of these will to solve, let's rewrite why? In a form that's more easily differentiable. So we have Y equals for each of the T. Either to t minus for each of the t V, the T. Or more simply for each of the three t minus for each of the two T. Thus we can simply apply rule zero to solve this. So we have Dy DT is equal to 14 of the three t times the u d x three minus four each of the two t time dutt. To simplifying, we have final solution. DY DT is equal to 12 each of the three t minus eight each of the two t.

View More Answers From This Book

Find Another Textbook

Numerade Educator

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 derivatives of the functions.\begin{equation}f(t)=\frac{t^{…

Find the derivative of the function.$y=e^{-2 t} \cos 4 t$

Find derivatives of the functions defined as follows.$$y=e^{4 x}$$

Derivatives Find and simplify the derivative of the following functions.…

Find derivatives of the functions defined as follows.$$y=4 e^{2 x^{2}-4}…

Find derivatives of the functions defined as follows.$$y=\frac{t e^{t}+2…

Find the derivative of the following functions.$$s(t)=4 e^{t} \sqrt{t}$$…

Find derivatives of the functions defined as follows.$$y=\frac{t^{2} e^{…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.