Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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![### Calculus: Derivative of a Function
In this exercise, we are asked to find the derivative of a given function \( g(t) \).
The function \( g(t) \) is defined as follows:
\[ g(t) = (8t + 8)^2 (8t^2 - 8)^{-3} \]
To find the derivative \( g'(t) \), we need to apply the product rule and chain rule of differentiation.
Below is a blank space provided to fill in the resulting expression for \( g'(t) \):
\[ g'(t) = \boxed{} \]
For those who are not familiar with the rules mentioned:
- **Product Rule**: If you have a function \( h(t) = u(t) \cdot v(t) \), then the derivative \( h'(t) = u'(t) \cdot v(t) + u(t) \cdot v'(t) \).
- **Chain Rule**: If you have a composite function \( y = f(u(t)) \), the derivative is \( \frac{dy}{dt} = \frac{dy}{du} \cdot \frac{du}{dt} \).
To proceed with solving, break down the function into parts and apply these rules accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54a9d33b-c075-4af5-8013-3f49004b10ba%2Fee91ba7b-296e-4298-9e62-efe2f46fed2f%2Fv6b9k3i_processed.png&w=3840&q=75)
Transcribed Image Text:### Calculus: Derivative of a Function
In this exercise, we are asked to find the derivative of a given function \( g(t) \).
The function \( g(t) \) is defined as follows:
\[ g(t) = (8t + 8)^2 (8t^2 - 8)^{-3} \]
To find the derivative \( g'(t) \), we need to apply the product rule and chain rule of differentiation.
Below is a blank space provided to fill in the resulting expression for \( g'(t) \):
\[ g'(t) = \boxed{} \]
For those who are not familiar with the rules mentioned:
- **Product Rule**: If you have a function \( h(t) = u(t) \cdot v(t) \), then the derivative \( h'(t) = u'(t) \cdot v(t) + u(t) \cdot v'(t) \).
- **Chain Rule**: If you have a composite function \( y = f(u(t)) \), the derivative is \( \frac{dy}{dt} = \frac{dy}{du} \cdot \frac{du}{dt} \).
To proceed with solving, break down the function into parts and apply these rules accordingly.
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