Question

Find the derivative of e^x^2.

(a) e^x^2

(b) 2x

(c) 2e^x^2

(d) 2xe^x^2

The question was asked in an international level competition.

The origin of the question is Derivatives topic in section Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct answer is (d) 2xe^x^2

To elaborate: We apply chain rule. First we differentiate x^2.

\(\frac{d}{dx}\) (x^2) = 2x

Now, we know that \(\frac{d}{dx}\) (e^x) = e^x

We differentiate e^x^2 in the same manner and then multiply with the derivative of x^2

\(\frac{d}{dx}\) (e^x^2) = 2xe^x^2