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 the amplitude of y=1/2 sin2x
What were the major causes of WWII? Please include at least 4 answers.
Simplify the expressions: cot 0 sec 0 A. Sin0 B. Csc0 C. Cos0 D. Cos* 0
How do you?...Multiply out and simplify 10(2x-1)-20x?
What is the least common denominator for 5/6 and 3/8. 3/4 and 6/7
Why is sodium sulphate hemihydrate called as "Plaster of Paris"?
The function of the eardrum in the middle ear is to
Simplify the expressions: cot 0 sec 0 A. Sin0 B. Csc0 C. Cos0 D. Cos* 0
what is a high structure part of a church which has 5 letters
What is the least common denominator for 5/6 and 3/8. 3/4 and 6/7