Answers

The Brainliest Answer!
2015-05-04T16:38:42+05:30
 Take the derivative a few times and look for a pattern. 

For example, we can find the derivative of f(x) = e^(3x) this way: 

f(x) = e^(3x) 
f ' (x) = 3e^(3x) 
f '' (x) = 9e^(3x) 
f ''' (x) = 27e^(3x) 
f^(4) (x) = 81e^(3x) 

It looks like the pattern is that, each time we take the derivative, we multiply the function we had before by 3. 

Multiplying f(x) by 3 fifty times gives (3^50)e^(3x). 

So the 50th derivative of e^(3x) is (3^50)e^(3x). 
3 5 3
yeah when it comes
KKKKK
nice answer :3
you might be knowing but i guess its worth mentioning: e^x is the only function such that f^n(x)=f(x)
mmmmm
2015-05-06T02:05:59+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
We find the 1st derivative , then the second derivative, and so on...
We could find a pattern of the n th derivative.

f(x) = a x^n            a and n are constants.

if n < 50,    f ⁵°  = 0
if n = 50  ,  f ⁵°  = 50! * a
if n > 50,    f ⁵°  = n (n-1)..(n-49) a x^(n-50)
=========================
f(x) = a Sin bx

f ' = a b cos bx
f '' = - a b² Sin bx = - b² f
f ³ = - a b³ Cos bx  = - b² f '
f ⁴ = a b⁴ Sin bx  = - b² f '' = b⁴ f
f ⁵ =  a b⁵ Cos bx = - b² f ³  =
f ⁶ = - a b⁶ Sin bx  = - b² f ⁴ = - b⁶ f
f ⁷ = - a b⁷ Cos bx = - b² f ⁵
f ⁸ = a b⁸ Sin bx  = b⁸ f

so  f ⁴⁸ =  b⁴⁸ f
  f ⁴⁹ = b⁴⁹ a Cos bx
  f ⁵° = - b⁵° a Sin bx = - b⁵° f
==========================
f(x) = Log ax

 f ' = a x⁻¹          f '' = - a x⁻²            f ³ = 2 a x⁻³        f ⁴ = - 3! x⁻⁴
so  f ⁵° = - 49! x⁻⁵°

1 5 1
please click on thanks blue button above