Question

Differentiate 3e^3x^3 w.r.t x.

(a) 27x^-2 e^3x^3

(b) 27x^2 e^3x^3

(c) -27x^2 e^3x^3

(d) -27x^-2 e^3x^3

The question was posed to me during an online exam.

My doubt stems from Exponential and Logarithmic Functions in portion Continuity and Differentiability of Mathematics – Class 12

Answer 1

Correct answer is (b) 27x^2 e^3x^3

To explain: Consider y=3e^3x^3

\(\frac{dy}{dx}\)=\(\frac{d}{dx}\)(3e^3x^3)

\(\frac{dy}{dx}\)=3e^3x^3 \(\frac{d}{dx}\)(3x^3)

\(\frac{dy}{dx}\)=3e^3x^3 (3(3x^2))

\(\frac{dy}{dx}\)=27x^2 e^3x^3.