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
$2x$
C
${2e^x}^2$
✓
${2xe^x}^2$
✓
Answer
Correct option: D.
${2xe^x}^2$
We apply chain rule. First we differentiate $x^2$.
$\frac{\text{d}}{\text{dx}} (\text{x}^2) = 2\text{x}$
Now, we know that $\frac{\text{d}}{\text{dx}} (\text{e}^x) = \text{e}^\text{x}$
We differentiate ${e^x}^2$ in the same manner and then multiply with the derivative of $x^2$
$\frac{\text{d}}{\text{dx}} (\text{e}^\text{x}) = 2\text{x}\text{e}^\text{x}$
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