Discussion
The \( n \)th derivative of \( e^{ax} \) is
Answer: D
Each differentiation multiplies by the constant \( a \) and leaves the exponential alone, so after \( n \) steps
\[ \frac{d^{n}}{dx^{n}} e^{ax} \;=\; a^{n} e^{ax}. \]
This is why the exponential is the natural basis for linear differential equations: substituting it turns each derivative into a power of \( a \) and the equation into a polynomial
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development