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Prove that $ \frac {d}{dx}$ (cot $ x $) = $ - csc^2 x. $
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00:41
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Missouri State University
Campbell University
Harvey Mudd College
Baylor University
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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he It's clear, so enumerated here. So we're gonna do a proof We're gonna start off with our code tangent. So de over de ex coat engine of hacks. Another way to right. This is D over D x of co sign over sign, which is equal to sign when we apply the quotient. Cool de over de ex co sign minus co sign D over the access sign well over sign square. This becomes equal to sign times Negative sign dryness Co sign turns co signed over signed square, which is equal to negative Signed Square Plus Co signed square over a sign square. This becomes equal to negative one for trig identities over sign at square, which is equal to negative co Sika Square.
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