graciewarren1498 graciewarren1498
  • 03-10-2017
  • Mathematics
contestada

If f(x) = f(x)g(x), where f and g have derivatives of all orders, show that f'' = f ''g + 2f 'g' + fg''.

Respuesta :

LammettHash
LammettHash LammettHash
  • 03-10-2017
Differentiating once, we have

[tex]f'(x)=f'(x)g(x)+f(x)g'(x)[/tex]

Differentiating again,

[tex]f''(x)=f''(x)g(x)+f'(x)g'(x)+f'(x)g'(x)+f(x)g''(x)[/tex]
[tex]f''(x)=f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x)[/tex]

as needed.
Answer Link

Otras preguntas

What is affirmative action?
create environmental slogans for your city or town.
can't be brothers. help please
what were the effects of dred scott v. sandford?
If something is volatile, it _____ easily. A. cools B. melts C. liquefies D. evaporates
Which parts of the frog nervous system can be observed in its abdominal cavity and hind leg
One of the products of a fermentation reaction is
a diamond has a density of 3.5 g/cm what is the mass of a diamond with a volume of 3.0cm
Complete the following statement: The Triangle Shirtwaist fire played an important role in a. bringing about labor reforms in the United States. b. bringing a
The enclosure movement helped to bring about the industrial revolution by increasing the what ?