Limits and Derivatives — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
Find the derivative of $ e^{x^2} $:
A
$ e^{x^2} $
B
$2^x$
C
$ 2 e^{x^2} $
✓
$2xe^{x^2}$
✓
Answer
Correct option: D.
$2xe^{x^2}$
We apply chain rule.
First we differentiate $x^2$.
$\frac{\text{d}}{\text{dx}} (x^2 ) = 2\text{x}$
Now, we know that $\frac{\text{d}}{\text{dx}}(e^x ) = e^x$
We differentiate $ex^2$ in the same manner and then,
multiply with the derivative of $\frac{{\text{x}}^2 \text{d}}{\text{dx} (\text{e}^{x^2})} = \text{2xe}^{x^2}.$
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