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Find the derivative of the function.$ g(x) = (2ra^{rx} + n)^P $

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00:22

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Fan Y.

October 10, 2019

it is wrong

Saad A.

March 4, 2019

Missouri State University

Oregon State University

Harvey Mudd College

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.

04:51

Find the derivative of the…

02:52

find the derivative of the…

00:48

01:15

Differentiate the function…

05:34

Find the $n$ th derivative…

02:12

04:20

Okay, here we have a chain rule problem, and it looks like there was a shortage of numbers for this problem. And so somebody had to write it with a whole bunch of letters. But we're going to use all the same concepts and just apply all the rules we already know. So to find the derivative, the outermost layer is the P power. And so we're going to bring down the P and raise the inside to the P minus one, just like if that was a three or a four, you'd bring down that number and you'd raise it to the one less power. Now we need to multiply by. The derivative of the Insight and the insight is a sum of two terms. So we'll find the derivative of the first term, plus the derivative of the second term. So now we're finding the derivative of to our times a to the Rx, and so too are is just a constant are that are variable. Here is X. So all the other later letters are constants. So we leave. The two are the constant and we multiply it by the derivative of a to the Power Rx well, remember the derivative of a to the X is age the X Times natural law, gay. So if it's a to the Rx using the chain rule, the derivative would be a to the Rx Times natural log a times a derivative of our X, which is our So we get a to the Rx times natural law. Gay times are so that takes care of that. And then we have plus the derivative of n But an is just a constant. So it's driven of a zero. So we're actually not adding anything to that. Now let's see if there's anything we can do to this to make it a little bit nicer. Niedere Well, I suppose we could multiply the P and the two are and they are together. So we have to r squared P, and then we have the natural log of a as well. And then we have the big quantity here. We'll just rewrite it to our age of the R X plus n to the P minus one. And we still have the A to the Rx two, right, So a lot of it was just copying the same thing all over again.

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