+0  
 
0
43
2
avatar

What is the f''(x) of (x/(x2+2))

 

I tried using the calculato by web 2.0 but I think it's incorrect.

Guest Aug 5, 2017
edited by Guest  Aug 5, 2017
Sort: 

2+0 Answers

 #1
avatar
0

Possible derivation:
d/dx((x f''(x))/(2 + x^2))
Use the quotient rule, d/dx(u/v) = (v ( du)/( dx) - u ( dv)/( dx))/v^2, where u = x f''(x) and v = x^2 + 2:
 = ((2 + x^2) (d/dx(x f''(x))) - x (d/dx(2 + x^2)) f''(x))/(2 + x^2)^2


Use the product rule, d/dx(u v) = v ( du)/( dx) + u ( dv)/( dx), where u = x and v = f''(x):
 = ((2 + x^2) x (d/dx(f''(x))) + (d/dx(x)) f''(x) - x (d/dx(2 + x^2)) f''(x))/(2 + x^2)^2
The derivative of f''(x) is f^(3)(x):
 = (-x (d/dx(2 + x^2)) f''(x) + (2 + x^2) (f^(3)(x) x + (d/dx(x)) f''(x)))/(2 + x^2)^2


Differentiate the sum term by term:
 = (-x f''(x) d/dx(2) + d/dx(x^2) + (2 + x^2) ((d/dx(x)) f''(x) + x f^(3)(x)))/(2 + x^2)^2
The derivative of 2 is zero:
 = (-x (d/dx(x^2) + 0) f''(x) + (2 + x^2) ((d/dx(x)) f''(x) + x f^(3)(x)))/(2 + x^2)^2


Simplify the expression:
 = (-x (d/dx(x^2)) f''(x) + (2 + x^2) ((d/dx(x)) f''(x) + x f^(3)(x)))/(2 + x^2)^2
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2: d/dx(x^2) = 2 x:
 = (-x f''(x) 2 x + (2 + x^2) ((d/dx(x)) f''(x) + x f^(3)(x)))/(2 + x^2)^2


Simplify the expression:
 = (-2 x^2 f''(x) + (2 + x^2) ((d/dx(x)) f''(x) + x f^(3)(x)))/(2 + x^2)^2
The derivative of x is 1:
Answer: | = (-2 x^2 f''(x) + (2 + x^2) (1 f''(x) + x f^(3)(x)))/(2 + x^2)^2

Guest Aug 5, 2017
 #2
avatar+25995 
+3

"What is the f''(x) of (x/(x2+2))"

 

.

Alan  Aug 5, 2017

8 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details