Answer to Question #209211 in Calculus for Akhona Klanisi

Question

Question  3

Differentiate the function

f (x) = 3x³e^2x.

a. 5x⁴e^3x

b. 3x²e^2x(x − 3)

c. 3e^3x + 9x⁴x⁵

d. 3x²e^2x(2x + 3)

Answer 1

$$f (x) = 3x^3e^{2x}$$

$$f'(x)=3(3x^2)e^{2x}+3x^3(2)e^{2x}=3x^2e^{2x}(2x+3)$$

d. $3x^2e^{2x}(2x+3)$