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Differentiate $ f $ and find the domain of $ f. $
$ f(x) = \sqrt {2 + \ln x} $
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00:56
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 6
Derivatives of Logarithmic Functions
Derivatives
Differentiation
Campbell University
Baylor University
Boston 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.
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Differentiate $f$ and find…
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In this problem we are given a function anywhere find derivative and the domain of this function less tarriere, a prime effect is we have 2 operators. First 1 is the square root. Second 1. Is initial x we're going to start from 1, so the derivative of square root would be 1 over 2 square root, 2 plus natural log of x. We'Re going to multiply this with the derivative of inner function, which is on our x, so we find the derivative. Then the 1 over 2 x times square root of 2 plus natural log of x, all right now we're going to decide on the domain on. We have a square root of 2 plus natural log of x, and we know that square root, 2 plus natal log of x should be positive, or else we wouldn't be in that wouldn't be a real number of function values. So it means that 2 plus natural log of x should be greater than 0, so natural log of x should be greater than negative. 2 x should be greater than e to the negative 2. So from this we see that the rain of this function is time to the negative 2 to positive infinity.
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