Question

Find d/dx(e^3ln(x)).
a. e^3lnx
b.e^3ln(x)/x
c.3e^3lnx
d.3x^2

Answer 1

D. 3x²

General Formulas and Concepts:

Algebra II

• If you raise e to the natural log, they cancel out and vice versa

Calculus

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

`f(x)=e^(3lnx)`

Step 2: Rewrite

`f(x) = x^3`

Step 3: Take Derivative

1. Basic Power Rule: f'(x) = 3x³⁻¹
2. Simplify: f'(x) = 3x²