Question

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

Answer 1

Answer:

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

Step-by-step 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