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

When 70,000 is written as 7.0 10^{n} what is the value of n ? Can you please explain with some details?
Can you explain 3x+4/5=7/10. Solve
How did professors feelings about black well as a student change over time?
What is twenty percent off 600 hundred pounds
how much sperm does it take to make a baby?
A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumptio
how much sperm does it take to make a baby?
What is the value of 6P6?  A.1  B.36  C.720  D.46,656
type the requested verb form of this verb. future progressive tense: soar
what kind of symbiotic relationship is showm between Dori and Marlin