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Find $ f'(x) $ and $ f"(x). $
$ f(x) = \sqrt{x}e^x $
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01:18
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Missouri State University
Campbell University
University of Michigan - Ann Arbor
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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Find $ f'(a) $.
it's clear is suing you right here. So I'm gonna take the derivative. We're gonna apply the product. Cool. So we have tea over DX X. It's the 1/2 power eats backs Just becomes equal to next to the one have power de over de X e to the X plus each The x d over d x next to the one have this is equal to eat The X Times X to the 1/2 was one have x the negative one have for the second derivative We're gonna apply the product will when we get next. The 1/2 plus one have x to the negative one. Have d over d X for each The X plus e to the x d over DX next to the one have plus 1/2 x to the negative Have we simplify only get hey x Times X tonic 1/2 plus 1/2 x to the negative 1/2 plus e to the x one Have X It's the negative one have plus 1/2 times negative When have X the negative three House This becomes equal to eat The X hands X to the one have less extra negative 1/2 minus 1/4 ex to the negative 3/2
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