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Differentiate the function.

$ g(t) = \sqrt {1 + \ln t} $

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00:20

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Missouri State University

Campbell University

Oregon State University

Harvey Mudd College

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.

02:37

Differentiate the function…

0:00

01:43

01:16

In this problem we are asked to find the avatar of 1 plus natural tree, so the outer function or the vale of pressure here is ferron inside we have more posnania while finding derivative we're going to start from the outer oppression. So derivative of square root, which is 1 over 2 square root of 1 plus initial left t not multiply this by the therese inner function, which is 1 plus natural love of t that is 1 over 2 square root of 1 plus natural log of t multiplied By 1 over t, so we can write the derivative prime of theta as 1 over 2 t times square root of 1 plus negatur log of t.

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