7. f'(m) for f(m)= 1 sec(2m) 9. f"(x) for f(x) = 3x-25* 11. f'(I) for f(T) = BT + rº 1-B dy 13. 3. d for y= In √5 + x² dt 15. g'(x) for g(x)=x-e*| 6. f'(x) for f(x) = sinh(x² +1) 8. f'(t) for f(t) = sin (²) 10. g'(0) for g(0)=tan(50) 12. f'(x) for f(x)=xcos (√x+1) dy 14. for y = (cotl+cotu) du 16. g'(z) for g(z)=- az a² +2²°
7. f'(m) for f(m)= 1 sec(2m) 9. f"(x) for f(x) = 3x-25* 11. f'(I) for f(T) = BT + rº 1-B dy 13. 3. d for y= In √5 + x² dt 15. g'(x) for g(x)=x-e*| 6. f'(x) for f(x) = sinh(x² +1) 8. f'(t) for f(t) = sin (²) 10. g'(0) for g(0)=tan(50) 12. f'(x) for f(x)=xcos (√x+1) dy 14. for y = (cotl+cotu) du 16. g'(z) for g(z)=- az a² +2²°
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Questions 10 and 11 please.
![### Calculus Derivatives Exercise
This exercise involves finding derivatives of various functions. Each item specifies a function and requires you to find its derivative. Here is the list of problems presented in mathematical format:
1. **\( f'(m) \) for \( f(m) = \frac{1}{\sec(2m)} \)**
2. **\( f'(x) \) for \( f(x) = \sin(kx + t) \)**
3. **\( f'(t) \) for \( f(t) = \sin^{-1}\left(\frac{1}{2}\right) \)**
4. **\( f'(x) \) for \( f(x) = 3x - 2x^2 \)**
5. **\( f'(T) \) for \( f(T) = \frac{\beta T + \Gamma^6}{1 - \beta} \)**
6. **\( \frac{dy}{dt} \) for \( y = \ln\sqrt{5 + x^2} \)**
7. **\( \frac{dy}{du} \) for \( y = (\cot u + \cot u)^x \)**
8. **\( f'(x) \) for \( f(x) = x \cos(\sqrt{3x + 1}) \)**
9. **\( g'(\theta) \) for \( g(\theta) = \sqrt[3]{\tan(5\theta)} \)**
10. **\( g(x) \) for \( g(x) = \lvert x \cdot e^t \rvert \)**
11. **\( g(z) \) for \( g(z) = \frac{e^{az}}{a^2 + z^2} \)**
These problems test your understanding of calculus concepts, particularly differentiation. Focus on applying the rules of derivatives, including the power rule, product rule, chain rule, and derivatives of trigonometric and inverse trigonometric functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fac6bec-f0b2-4056-963f-cf73547656d5%2F53ebb692-e134-4bdc-9db7-db1fb8e1d379%2Fsbqhnrv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculus Derivatives Exercise
This exercise involves finding derivatives of various functions. Each item specifies a function and requires you to find its derivative. Here is the list of problems presented in mathematical format:
1. **\( f'(m) \) for \( f(m) = \frac{1}{\sec(2m)} \)**
2. **\( f'(x) \) for \( f(x) = \sin(kx + t) \)**
3. **\( f'(t) \) for \( f(t) = \sin^{-1}\left(\frac{1}{2}\right) \)**
4. **\( f'(x) \) for \( f(x) = 3x - 2x^2 \)**
5. **\( f'(T) \) for \( f(T) = \frac{\beta T + \Gamma^6}{1 - \beta} \)**
6. **\( \frac{dy}{dt} \) for \( y = \ln\sqrt{5 + x^2} \)**
7. **\( \frac{dy}{du} \) for \( y = (\cot u + \cot u)^x \)**
8. **\( f'(x) \) for \( f(x) = x \cos(\sqrt{3x + 1}) \)**
9. **\( g'(\theta) \) for \( g(\theta) = \sqrt[3]{\tan(5\theta)} \)**
10. **\( g(x) \) for \( g(x) = \lvert x \cdot e^t \rvert \)**
11. **\( g(z) \) for \( g(z) = \frac{e^{az}}{a^2 + z^2} \)**
These problems test your understanding of calculus concepts, particularly differentiation. Focus on applying the rules of derivatives, including the power rule, product rule, chain rule, and derivatives of trigonometric and inverse trigonometric functions.
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