MHT CET202522 Apr 2025Morning ShiftMathematicsDifferentiationActual
For N N , d ^ n ~d x^ n ( x)=
Options
- A(n-1)! x^n
- Bn ! x^ n
- C( n -2)! x^ n
- D(-1)^ n -1 ( n -1)! x^ n
Correct answer
D. (-1)^ n -1 ( n -1)! x^ n
Step-by-step solution
Let y = x and consider its n th derivative d^n dx^n ( x) . The first derivative is d dx ( x) = x⁻¹ . Differentiating further reveals the pattern: d^2 dx^2 ( x) = -x⁻² d^3 dx^3 ( x) = 2x⁻³ d^4 dx^4 ( x) = -6x⁻⁴ This establishes the general formula: d^n dx^n ( x) = (-1)^ n-1 (n-1)! x^n Among the options, this corresponds to choice D .