Find d^2 y d x^2 if, y = e ^ (2 x +1) - Vidyadip

Question

Find $\frac{d^2 y}{d x^2}$ if,
$
y = e ^{(2 x +1)}
$

✓

Answer

$
y=e^{(2 x+1)}
$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{d y}{d x} & =\frac{d}{d x}\left[e^{(2 x+1)}\right]=e^{(2 x+1)} \cdot \frac{d}{d x}(2 x+1) \\
& =e^{(2 x+1)} \times(2 \times 1+0)=2 e^{(2 x+1)}
\end{aligned}
$
Differentiating again w.r.t. $x$, we get
$
\begin{aligned}
\frac{d^2 y}{d x^2} & =\frac{d}{d x}\left[2 e^{(2 x+1)}\right]=2 \frac{d}{d x}\left[e^{(2 x+1)}\right] \\
& =2 e^{(2 x+1)} \cdot \frac{d}{d x}(2 x+1)=2 e^{(2 x+1)} \times(2 \times 1+0) \\
& =4 e^{(2 x+1)} .
\end{aligned}
$

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