Question

Match the given functions in the first column with their first derivatives in the second column.

• A. $a^x\left(lo{g}_{e}a\right)$
• B. $\frac{1}{x},x>0$
• C. $n{x}^{n-1}$
• D. $e^x$

Answer 1

These are standard functions whose derivatives are mentioned in the videos. In case you cannot recall them, you can use derivatives by first principle to evaluate them.

The correct derivatives are as follows:

$x^n\to n{x}^{n-1},nisaconstant{e}^x\to e^x{a}^x\to a^{x}lo{g}_{e}a,a>0lo{g}_{e}x\to \frac{1}{x},x>0anothercaseforthefunctiongivenaboveislo{g}_{a}x\to \frac{1}{x}\left(lo{g}_{a}e\right)$