find third derivate f(x)=x/x+1
As typed, without parenthesis
f(x) = x/x + 1
f' = 0
In google type: calc101
When you see list of resultc click on:
Calc101com Automatic Calculus and Algebra Help
When page be open clik option: derivatives
When this page be open in rectacangle type:
x/(x+1)
and click options DO IT
You will see solution step-by-step
By the way on this site you can practice any kind of derivation.
P.S.
Third derivate is derivate of second derivate.
To find the third derivative of the function f(x) = x/(x+1), we will follow these steps:
Step 1: Differentiate the function once to get the first derivative f'(x).
Step 2: Differentiate the first derivative again to get the second derivative f''(x).
Step 3: Differentiate the second derivative again to get the third derivative f'''(x).
Let's start with Step 1:
To find f'(x), we will use the quotient rule, which states that for functions f(x) = u(x)/v(x), the derivative is given by:
f'(x) = (u'(x)v(x) - u(x)v'(x))/[v(x)]^2,
where u'(x) represents the derivative of u(x) and v'(x) represents the derivative of v(x).
For f(x) = x/(x+1), we have:
u(x) = x
v(x) = x+1
Now, we differentiate u(x) and v(x) separately:
u'(x) = 1 (the derivative of x is 1)
v'(x) = 1 (the derivative of x+1 is 1)
Using the quotient rule, we can find f'(x):
f'(x) = (1*(x+1) - x*1)/(x+1)^2
= (x+1 - x)/(x+1)^2
= 1/(x+1)^2
Moving on to Step 2:
To find f''(x), we will differentiate f'(x) using the power rule.
For the function g(x) = 1/(x+1)^2, the derivative is given by:
g'(x) = -2/(x+1)^3
Therefore, f''(x) = -2/(x+1)^3
Finally, Step 3:
To find f'''(x), we differentiate f''(x) using the power rule once again.
For the function h(x) = -2/(x+1)^3, the derivative is given by:
h'(x) = 6/(x+1)^4
So, the third derivative f'''(x) = 6/(x+1)^4
Therefore, the third derivative of f(x) = x/(x+1) is f'''(x) = 6/(x+1)^4.