Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find the derivatives of the given functions.$$y=e^{-3 x} \sec 4 x$$

$\frac{d y}{d x}=4 e^{-3 x} \sec 4 x \tan 4 x-3 e^{-3 x} \sec 4 x$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 6

Derivative of the Exponential Function

Derivatives

Missouri State University

Campbell University

Harvey Mudd College

University of Nottingham

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:41

Find derivatives of the fu…

01:38

00:51

01:02

04:26

Find the derivatives of th…

00:56

02:02

01:26

00:29

01:28

Find the first and second …

I We want to find dy dx for the function Y equals E to the negative three X times C can't four X. We're gonna rely on derivatives shortcuts to solve, particularly rule zero through three. Are listed here on the left. Rule zero is GDX Bu equals B D U L n D V d X G X E v u E d d d X. Rules one through the power rule. Product rule in general, respectively. Why equals negative three extent seek and four X. Has already written it's most easily differential form so we can proceed straight to the derivative. So we're gonna have to apply the product rule separating out of the room is repeated negative three X and four X. This gives for the derivative, Dy dx equals negative X. Three X times negative three. By rule 0, 10 C. Can four X plus either negative three X and four X and four X times for the derivative C can't is seeking tangent. So we've used that derivative plus the chain rule on the right hand side. Thus we have d i d x equals negative three X tents. You cant forex tens, 4, 10 4 x minus three.

View More Answers From This Book

Find Another Textbook

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 derivatives of the functions defined as follows.$$y=(x+3)^{2} e^{4 …

Find derivatives of the functions defined as follows.$$y=-4 e^{-0.3 x}$$…

Find the derivatives of the functions.$$y=(4 x+3)^{4}(x+1)^{-3}$$

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

Find derivatives of the functions defined as follows.$$y=\left(3 x^{3}-4…

Find the derivatives of the functions.$$y=x e^{-x}+e^{x^{3}}$$

Find the derivatives of the following functions.$$f(x)=\left(4-x^{2}\rig…

Find the first and second derivatives.$$y=\frac{4 x^{3}}{3}-x+2 e^{x}$$<…

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.