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Differentiate the function.
$ y = \ln \mid 1+ t - t^3 \mid $
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01:04
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 6
Derivatives of Logarithmic Functions
Derivatives
Differentiation
Missouri State University
University of Michigan - Ann Arbor
Idaho State 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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$ y…
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In this problem, we rest to find a derivative of metal work of absolute value of 1, plus t minus t cube for in our text book. We know that d d, t of absolute value of t, is equal to 1 over t, so we're just going to take derivative of this function as if we have no absolute value so why pem will then be natural log of 1 over 1 plus t minus T cube multiplied by derivation inner function, which is 1 minus 3 t square from the speed. I find the derivative to be 1 minus 3 t square divided by 1, plus t minus t c.
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