Question

${∆}^2\left(3e^x\right)$is equal to

• A. $3e^x$
• B. $3\left(h-1\right)e^x$
• C. $3{\left(e^h-1\right)}^2{e}^x$
• D. none of these

Answer 1

The correct option is C

$3{\left(e^h-1\right)}^2{e}^x$

Explanation for the correct option:

Given, ${∆}^2\left(3e^x\right)$

$$\begin{gathered} =3∆\left(∆e^x\right) \\ =3∆\left(e^{x+h}-e^x\right)\left(\because ∆e^x=\left(e^{x+h}-e^x\right)\right) \\ =3∆e^x\left(e^h-1\right) \\ =3\left(e^{x+h}-e^x\right)\left(e^h-1\right) \\ =3e^x\left(e^h-1\right)\left(e^h-1\right) \\ =3{\left(e^h-1\right)}^2{e}^x \end{gathered}$$

Hence, correct answer is option $\left(C\right)$