Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question
Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]3 Marks
Question
Find $\frac{ d ^2 y}{ d x^2}$, if $y = e ^{(2 x+1)}$
✓
Answer
$y=e^{(2 x+1)}$
Differentiating both sides w.r.t. $x$, we get
$ \frac{ d y}{ d x}= e ^{(2 x+1)} \cdot \frac{ d }{ d x}(2 x+1)$
$\therefore \frac{ d y}{ d x}= e ^{(2 x+1)} \cdot(2+0)$
$\therefore \frac{ d y}{ d x}=2 e ^{(2 x+1)} $
Again, differentiating both sides w.r.t. x, we get
$ \therefore \frac{ d ^2 y}{ d x^2}=2 \cdot \frac{ d }{ d x} e ^{(2 x+1)}$
$=2 e ^{(2 x+1)} \cdot \frac{ d }{ d x}(2 x+1)$
$=2 e ^{(2 x+1)} \cdot(2+0) $
$\therefore \frac{ d ^2 y}{ d x^2}=4 e ^{(2 x+1)}$
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