Question

Match the following
$\begin{array}{cc}Functions& Derivatives\\ \left(a\right)x^n& 1\left)\frac{1}{x}\right(lo{g}_{a}e)\\ \left(b\right)e^x& 2)\frac{1}{x},x>0\\ \left(c\right)a^x& 3)n{x}^{n-1},nisaconstant\\ \left(d\right)lo{g}_{e}x& 4)a^{x}lo{g}_{e}a,a>0\\ \left(e\right)lo{g}_{a}x& 5)e^x\end{array}$

• A. a – 1, b – 2, c – 3, d – 4, e – 5
• B. a – 1, b – 5, c – 4, d – 2, e – 3
• C. a – 3, b – 5, c – 4, d – 2, e – 1
• D. None of the above

Answer 1

The correct option is C

a – 3, b – 5, c – 4, d – 2, e – 1

These all are standard functions mentioned in the videos, where their derivatives were directly mentioned. In case you cannot recall a couple of them, you can use derivatives by first principle to evaluate them.
So the correct derivatives are as follows:
$x^n\to n{x}^{n-1},nisaconstant{e}^x\to e^x{a}^x\to a^{x}lo{g}_{e}a,a>0lo{g}_{e}x\to \frac{1}{x},x>0lo{g}_{a}x\to \frac{1}{x}\left(lo{g}_{a}e\right)$