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Find the derivative of the function.$ y = 2^{3^{4^{x}}} $

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$\ln 2 \ln 3 \ln 4 \cdot 2^{3^{x}} \cdot 3^{4^{x}} \cdot 4^{x}$

00:55

Frank Lin

01:51

Heather Zimmers

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

04:40

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.

44:57

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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01:43

Alright, what a funny looking problem. We have Y equals two to the three to the four to the X. And um it looks really scary so I'm gonna clean it up first and so what I'm gonna do is notice that when I have exponents two exponents you can multiply them. So basically I can think of this as two cubed to the four X. And that is eight to the four X. And that even I can read as eight to the four to the X. And eight to the fourth power is um 4096. So really that really scary looking function is just really 4096 to the X. Which I guess still looks a little scary. Okay so when I have uh an exponential function and I want to take the derivative uh then what I do is the rule is it looks like itself and then times at the end of the base. So um there we have it and there is our lovely derivatives. So hopefully that helps just kind of learning to use the, what goes on with exponents two exponents to be able to solve that quickly. So alright, have a wonderful day. See you next time

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