Chapter 10.2, Problem 1QR

To determine

To find: a formula for the n^thderivative of the function.

Answer to Problem 1QR

  $\left(2^n\right)e^{2x}$

Explanation of Solution

Given:

  $e^{2x}$

  $\left(2^n\right)e^{2x}$

For each successive derivative taken, another 2 is multiplied to $e^{2x}$ so that the n^th derivative would be multiplied by $2^n$ in accordance with the chain rule (the derivative of $2x$ is 2 ). $e^{2x}$ remains the same because the derivative of $e^{2x}$ is just $e^{2x}$ .