Answered: Evaluate and simplify y′. y = e6x sin…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.2: Trigonometric Functions Of Angles

Problem 34E

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Question

Evaluate and simplify y′.

y = e^6x sin x

Expert Solution

Step 1 Let us evaluate of given function

$G i v e n : y = e^{6 x} \sin x D i f f e r e n t i a t i o n o f P r o d u c t r u l e : \frac{d}{d x} (u v) = u' v + v' u H e r e, u = e^{6 x}, v = \sin x$

Step 2 Answer will be at end of step 2

$y = e^{6 x} . \sin x y' = 6 e^{6 x} . \sin x + e^{6 x} . \cos x y' = e^{6 x} (6 s i n x + c o s x)$

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