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

yes haha yes what no oh yeah no nevermind wait yes
100 POINTS 6 different answers needed, and a chart filled out I'll work on it on my own, but I do need some help and it would also be nice to compare my answe
What happened to Old Major? A. He died peacefully in his sleep. B .Mr. Jones sent him to a neighboring farm. C. Mr. Jones killed him for the meat. D. Mr. Jones
uld Carbon Dioxide be at its lowest level? A) July B) April C) January D) Ma What created the weather anomaly in the winter of 1980?
To apply for a job at the new store in the mole. is this a fragmentation sentence ​
Can someone help me? Im really bad at English ​
Please help! will mark brainliest i need an explanation to each road,a,b,c. ​
Im struggling with these 2 problems
plum-pudding model other name​
this is for medical detectives