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Differentiate.

$ y = c $ cos $ t + t^2 $ sin $ t $

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$$y^{\prime}=c(-\sin t)+t^{2}(\cos t)+\sin t(2 t)=-c \sin t+t(t \cos t+2 \sin t)$$

00:27

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

David L.

March 22, 2022

bro quit teaching u suck at this frank.

Campbell University

Baylor University

University of Nottingham

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.

02:32

$$\text { Differentiat…

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$ …

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Differentiate the function…

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Differentiate: = 2 Y cos (…

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03:43

Hey, it's clear. So when you right here. So we have Why equals c co sign t plus t square sign We're gonna differentiate when we get C times de over de ti of co sign plus t Square do you over DT no sign. Close sign T D over DT of T Square When we got negative C sign clean crust He square co signed plus two tea sign Oh, tea and we simplify more and we could take out sign of tea

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