If $y=a e^x+b e^{-x}+c$, where $a, b, c$ are parameters, then $y^{\prime \prime \prime}$ is equal to
If $y=a e^x+b e^{-x}+c$, where $a, b, c$ are parameters, then $y^{\prime \prime \prime}$ is equal to
- $0$
- $y$
- $y^{\prime}$
- $y^{\prime \prime}$
Solution
We have,
$
\begin{aligned}
y & =a e^x+b e^{-x}+c \\
y^{\prime} & =a e^x-b e^{-x} \\
y^{\prime \prime} & =a e^x+b e^{-x} \\
y^{\prime \prime \prime} & =a e^x-b e^{-x}=y^{\prime}
\end{aligned}
$
Asked in: AP EAMCET 2002
Practice more Differentiation questions on Aicharya