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

Which of the following are types of formatting you can apply to a spreadsheet? Choose all that apply.
A small amount of a solid is added to water. The observation made after fifteen minutes is shown in the figure. Which of these solids has been probably added
A hiker stands at an unknown elevation before he ascends 2 miles up a mountain to an elevation of 9 miles. Find the elevation of the hiker before his ascent.
Which of these was a result of the Labor Day hurricane that took place during the Great Depression? A) Farmers lost many orange trees in Orlando. B) Cattle ran
What is the x-intercept and y-intercept of the equation 2x+1. 2O POINTS!!!!!!
As you move from right to left on the periodic table the atomic radius _____ Fill in the blank
If the simple annual interest rate on a loan is 6, what is the interest rate in percentage per month?
Cost and benefit in economic example
what is chemistry and it applications
find the value of x. round the length to the nearest tenth