Differentiation of logx | derivative of log x | differentiation of log x |#differentiation |#shorts

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Издатель May 5, 2023

Differentiation of logx | derivative of log x | differentiation of log x |
In this YouTube shorts video, we will explore the process of differentiating the function (log x)^7. Differentiation is a fundamental concept in calculus, and it involves finding the rate at which a function changes. It is used in a wide range of applications, from physics and engineering to economics and finance.

Before we begin, let's first define what a logarithm is. A logarithm is an exponent to which a base must be raised to obtain a given number. For example, the logarithm base 10 of 100 is 2, because 10^2 = 100. The natural logarithm, denoted by ln, is a logarithm with base e, where e is a mathematical constant approximately equal to 2.71828.

Now, let's take a look at the function (log x)^7. To differentiate this function, we need to apply the chain rule, which is a rule for finding the derivative of a composite function. The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:

dy/dx = (dy/du) * (du/dx)

In this case, we can think of (log x)^7 as a composite function, where u = log x and y = u^7. Therefore, we have:

y = u^7
u = log x

Applying the chain rule, we get:

dy/dx = (dy/du) * (du/dx)
dy/dx = 7u^6 * (1/x)
dy/dx = 7(log x)^6 * (1/x)

So the derivative of (log x)^7 is 7(log x)^6 * (1/x). This means that the rate at which the function changes with respect to x is given by this expression.

Now, let's take a look at some of the keywords and tags that could be useful for this video:

Keywords:
- differentiation
- calculus
- logarithm
- chain rule
- composite function

Tags:
- #calculus
- #logarithm
- #chainrule

By including these keywords and tags in the description box of the video, it will make it easier for people who are searching for content related to differentiation, calculus, or logarithms to find the video. Additionally, using relevant tags can help the video appear in the "related videos" section of other videos on YouTube, which can help increase its visibility.

Overall, this YouTube shorts video provides a clear and concise explanation of how to differentiate the function (log x)^7. By using the chain rule and some basic algebra, we can obtain the derivative of this function as 7(log x)^6 * (1/x). This video is suitable for students or anyone who is interested in learning more about calculus and its applications.