Theorem: General Power Rule If u(x) is a differentiable function, n is any real number, and f(x) = [u(x)]", then 2-1 O f'(x) = n[u(x)] "-¹ u'(x) O f'(x)=n[u(x)]"-1 ○ f'(x) = n[u'(x)]"−¹ u(x) O f'(x)=(n-1)[u(x)]" u'(x) O f'(x)= [u(x)]"¹ u'(x)
Theorem: General Power Rule If u(x) is a differentiable function, n is any real number, and f(x) = [u(x)]", then 2-1 O f'(x) = n[u(x)] "-¹ u'(x) O f'(x)=n[u(x)]"-1 ○ f'(x) = n[u'(x)]"−¹ u(x) O f'(x)=(n-1)[u(x)]" u'(x) O f'(x)= [u(x)]"¹ u'(x)
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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![Theorem: General Power Rule
If u(x) is a differentiable function, n is any real number, and
f(x) = [u(x)]", then
2-1
O f'(x) = n[u(x)] "-¹ u'(x)
O f'(x)=n[u(x)]"-1
○ f'(x) = n[u'(x)]"−¹ u(x)
O f'(x)=(n-1)[u(x)]" u'(x)
O f'(x)= [u(x)]"¹ u'(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cac52cf-c19f-4e3d-a995-6f3c7099178c%2F60bdc44b-22c8-4d91-937c-90f2274804af%2F571m6j3_processed.png&w=3840&q=75)
Transcribed Image Text:Theorem: General Power Rule
If u(x) is a differentiable function, n is any real number, and
f(x) = [u(x)]", then
2-1
O f'(x) = n[u(x)] "-¹ u'(x)
O f'(x)=n[u(x)]"-1
○ f'(x) = n[u'(x)]"−¹ u(x)
O f'(x)=(n-1)[u(x)]" u'(x)
O f'(x)= [u(x)]"¹ u'(x)
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