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

$=e^{t \sin 2 t}(2 t \cos 2 t+\sin 2 t)$

00:32

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Harvey Mudd College

Baylor University

University of Nottingham

Idaho State University

Lectures

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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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