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

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

Question 3 of 10 how can onomatopoeia be used as a form of synesthesia? a. the sound of the word can imitate a visual effect. b. the sound of the word can imita

4. Which of the following statements about sentences is true? A. There are only two sentence patterns you can use to ask a question. B. The English language gen

What is the moral of the Epic of Gilgamesh What lesson did Gilgamesh learn?

What is national debt

What to do in 49 days after death?

help fast will give brainliest help help!!!! 20. a student constructed the accompanying elliptical orbit of a moon revolving around a planet. the foci of this

What did Jim sell to get the combs in the Gift of Magi?

Dakota spent $6.40, $12.25, and $8.60 for lunch over a three-day period. How much did she spend on lunch for these three days?

You have been hired to pour a concrete patio (i.e. your parents told you to do it correctly or be grounded for the rest of your life). they have requested that

Ali and Mel are making 3-digit codes. The digit 0 is not used. Ali only uses odd digits. Mel only uses even digits. Ali can make x more codes than Mel. Assume