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Differentiate.
$ f(t) = te^t $ cot $ t $
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00:54
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Oldens P.
October 8, 2021
y = x8 + cot(x)
Campbell University
University of Nottingham
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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It'S chlorinumerade here so we're going to take the derivative of t times e to the t times. Co tangent. This becomes equal to d over d t of t times e to the t times: co, tangent plus t it's chloris numerade here, so we're going to times d over dt of each of the t, co, tangent, plus t e to the t g over d. T of co tangent, which is equal to negative t e, take the derivative of t times e to the t times. Co tangent. This becomes equal to d over d t of t times e to the t times: co, tangent plus t to t co, secant square plus t e to the t, co, tangent of t plus e to the t, co, tangent of t. You simplify and we get e to the times d, over dt of e to the t, co, tangent, plus t e to the t g over d t of co tangent, which is equal to negative t e t, negative e to the times t co, secant square Plus negative t minus 1 co, tangent.
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