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Find the derivative of the function.$ F(t) = e^{t \sin 2t} $

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00:32

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Missouri State University

Oregon State University

Baylor 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 derivative of the…

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Differentiate the function…

03:28

Okay, let's find the derivative of capital f of tea. We have e to the power T sign of two T. And in general, the derivative of E to a function is each of the function times the derivative of the function. So this would be e to the t sign of two t times the derivative of tea. Sign of two t and t sign of two t is a product. So we need to use the product rule to find the derivative. So it would be the first tee times the derivative of the second, the derivative of Sinus co sign. So we have co sign to tee times the derivative of the inside the derivative of two tea is too. So that was chain rule right there. So we have the first times the derivative of the second plus the second sign of two t times. The derivative of the first derivative of tea is one. Okay, so we can write this as e to the T sign of two t times. Now will simplify this term here, and we'll call it to t co sign to t plus sign of two t

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