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Find an equation of the tangent line to the curve…
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Problem 50 Hard Difficulty

Find $ y' $ and $ y". $
$ y = e^{e^x} $

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00:33

Frank Lin

Related Courses

Calculus 1 / AB
Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Related Topics

Derivatives

Differentiation

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Top Calculus 1 / AB Educators
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Lectures

Video Thumbnail

04:40
Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
Video Thumbnail

44:57
Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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Video Transcript

okay. Our function here is why equals E to the E to the X, and we're going to use the chain rule to find the derivative The derivative of E to the G of X will be e to the G of X times J prime of X. So for white crime, we have the derivative of E to the each of the X, which is each of the each of the X times, the derivative of each of the X, which is he to the X? Okay, we could use exponents properties where if you have a to the end times a to the M, you get a to the end plus M and we could add the exponents on E. We could add the E to the X and the X, and another form of our answer would be e to the each of the X plus X power. And I think we'll use that as we find the second derivative. So second derivative again, the derivative of each of the G of X is e to the g of x times G prime of X. So the derivative will be e to the E to the X plus X times, the derivative of each of the X plus X and the derivative of that is each of the X plus one.

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
Grace He

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Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40
Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
Video Thumbnail

44:57
Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
Join Course
Recommended Videos

02:56

Find $y^{\prime}$ and $y^{\prime \prime}$. $y=e^{e^{x}}$

01:18

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05:20

Find $y^{\prime}$ if $e^{x / y}=x-y$

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Find $d y / d x$. $$ y=x e^{2}-e^{x} $$

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Find $d y / d x$. $$ y=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} $$

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Find $d y / d x$. $$ y=x^{2} e^{x}-x e^{x} $$

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Calculate $y^{\prime \prime}$ and $y^{\prime \prime \prime}$. $$ y=\frac{e^{x}}…
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