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Differentiate the function.

$ f(x) = \sin (\ln x) $

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00:13

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Missouri State University

Campbell University

Baylor University

Idaho State University

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.

01:58

Differentiate the function…

01:35

01:18

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00:59

00:55

In this problem were just to find derivative of sin of natural log of x. We'Re going to start from the outer function, which is sine of x or derivative, would be cosine. Natural log of x, multiplied by derivative 3 d x of the inner function. Natural lot x, that is cosine of natural log of x, divided by derivative of natural log of x, is 1 over x. So we have cos natural log of x, divided by.

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