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Find the given derivative by finding the first few derivatives and observing the pattern that occurs.$ \frac {d^{99}}{dx^{99}}(\sin x) $

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00:34

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Campbell 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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Find the given derivative …

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Find the derivative of the…

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$$\text { } , \text { …

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it's clear. So when you raid here, so we have the derivative, we calculate it, it becomes co sign second. Or if it is this negative sign, the searcher of it is. There's a negative co sign, and the fourth year of it is ISS Sign. The sister of it is ISCO sign again. So we see that repeats after the fourth time. So we're gonna get 99 and divide it by four to find the remainder, which gives us 24 and the remainder of three. So the 3rd 1 gives us negative co sign of X.

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