please help me find the derivative The image contains a handwritten mathematical function. The function is written as follows:\[ g(a) = 8^{-\frac{a}{3}} \cdot \sin(5a) \]This function defines $ g(a) $ in terms of the variable $ a $. It is composed of two main parts:1. $ 8^{-\frac{a}{3}} $ - This represents an exponential function with base 8 raised to the power of $-\frac{a}{3}$.2. $ \sin(5a) $ - This represents the sine function, where the argument is $ 5a $.To understand this function better:- As $ a $ changes, $ 8^{-\frac{a}{3}} $ will exponentially decrease if $ a $ increases because of the negative exponent.- The $ \sin(5a) $ function represents a periodic oscillation which remains bounded between -1 and 1, and oscillates more frequently due to the multiplication by 5.Combining these, $ g(a) $ will exhibit an oscillatory behavior modulated by an exponentially decaying factor as $ a $ increases.

Answered: Image /qna-images/answer/d7578f67-1b53-414c-aa3d-c38227af954d.jpg

Answered: gla) = 8 3 sin5a 11

Math

Calculus

gla) = 8 3 sin5a 11

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.4: Operations On Functions

Problem 123E

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Question

please help me find the derivative

The image contains a handwritten mathematical function. The function is written as follows:

\[ g(a) = 8^{-\frac{a}{3}} \cdot \sin(5a) \]

This function defines $ g(a) $ in terms of the variable $ a $. It is composed of two main parts:

1. $ 8^{-\frac{a}{3}} $ - This represents an exponential function with base 8 raised to the power of $-\frac{a}{3}$.
2. $ \sin(5a) $ - This represents the sine function, where the argument is $ 5a $.

To understand this function better:
- As $ a $ changes, $ 8^{-\frac{a}{3}} $ will exponentially decrease if $ a $ increases because of the negative exponent.
- The $ \sin(5a) $ function represents a periodic oscillation which remains bounded between -1 and 1, and oscillates more frequently due to the multiplication by 5.

Combining these, $ g(a) $ will exhibit an oscillatory behavior modulated by an exponentially decaying factor as $ a $ increases.

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