- #1
ttpp1124
- 110
- 4
- Homework Statement
- Finding the nth derivative.
- Relevant Equations
- n/a
Did I calculate this properly?
Last edited by a moderator:
The formula for finding the nth derivative of f(x) = x/(x+1) is (-1)^n * n! / (x+1)^(n+1).
To find the first derivative, we use the power rule and quotient rule. First, we rewrite the function as f(x) = x * (x+1)^(-1). Then, using the power rule, we get f'(x) = 1 * (x+1)^(-1) + x * (-1) * (x+1)^(-2). Simplifying, we get f'(x) = (x+1)^(-2) - x(x+1)^(-2). Finally, using the quotient rule, we get f'(x) = (x+1)^(-2) * (1 - x).
The nth derivative of f(x) = x/(x+1) will have n+1 terms.
Yes, the nth derivative can be simplified using algebraic manipulations and the properties of derivatives. For example, the second derivative can be simplified to f''(x) = 2(x+1)^(-3) * (1 - 2x).
The value of x affects the nth derivative of f(x) = x/(x+1) in that it determines the coefficients of each term. As x increases or decreases, the coefficients will change accordingly, resulting in a different nth derivative.