19. Suppose that u and v are functions of x that ar e differentiable x=0 and that %3D u(0) = 5, u'(0) = 3 v(0)% -1, v'(0) = 2. GARCEC IRDAY -F Find the values of the followving derivatives at x = 0. d. (a) (uv) dx dx v
19. Suppose that u and v are functions of x that ar e differentiable x=0 and that %3D u(0) = 5, u'(0) = 3 v(0)% -1, v'(0) = 2. GARCEC IRDAY -F Find the values of the followving derivatives at x = 0. d. (a) (uv) dx dx v
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with problems 19 (a) only
![**Using Numerical Values**
**19.** Suppose that \( u \) and \( v \) are functions of \( x \) that are differentiable at \( x = 0 \) and that:
\[
u(0) = 5, \quad u'(0) = 3
\]
\[
v(0) = -1, \quad v'(0) = 2
\]
Find the values of the following derivatives at \( x = 0 \).
(a) \(\frac{d}{dx}(uv)\)
(b) \(\frac{d}{dx}\left(\frac{u}{v}\right)\)
(c) \(\frac{d}{dx}\left(\frac{v}{u}\right)\)
(d) \(\frac{d}{dx}(7v - 2u)\)
**20.** Suppose that \( u \) and \( v \) are differentiable functions of \( x \) and that:
\[
u(1) = 2, \quad u'(1) = 0
\]
\[
v(1) = 5, \quad v'(1) = -1
\]
Find the values of the following derivatives at \( x = 1 \).
(a) \(\frac{d}{dx}(uv)\)
(b) \(\frac{d}{dx}\left(\frac{u}{v}\right)\)
(c) \(\frac{d}{dx}\left(\frac{v}{u}\right)\)
(d) \(\frac{d}{dx}(7v - 2u)\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ea8be2a-b1da-472d-bbc4-91d8ae774356%2Fde568563-6336-45ff-9e9b-249856a33712%2Fussv5iq.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Numerical Values**
**19.** Suppose that \( u \) and \( v \) are functions of \( x \) that are differentiable at \( x = 0 \) and that:
\[
u(0) = 5, \quad u'(0) = 3
\]
\[
v(0) = -1, \quad v'(0) = 2
\]
Find the values of the following derivatives at \( x = 0 \).
(a) \(\frac{d}{dx}(uv)\)
(b) \(\frac{d}{dx}\left(\frac{u}{v}\right)\)
(c) \(\frac{d}{dx}\left(\frac{v}{u}\right)\)
(d) \(\frac{d}{dx}(7v - 2u)\)
**20.** Suppose that \( u \) and \( v \) are differentiable functions of \( x \) and that:
\[
u(1) = 2, \quad u'(1) = 0
\]
\[
v(1) = 5, \quad v'(1) = -1
\]
Find the values of the following derivatives at \( x = 1 \).
(a) \(\frac{d}{dx}(uv)\)
(b) \(\frac{d}{dx}\left(\frac{u}{v}\right)\)
(c) \(\frac{d}{dx}\left(\frac{v}{u}\right)\)
(d) \(\frac{d}{dx}(7v - 2u)\)
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