Question

What is the derivative of \[{{e}^{3}}\]?

Answer 1

Hint: In this type of question we have to use basic rules of derivatives. We know that the derivative is the measure of the rate of change of a function. Also we know that the derivative of a constant is zero. When we consider the derivative of any function if it is not specified then by default it is with respect to x. If there is no any x in the expression then that expression can be termed as a constant.

Complete step-by-step answer:
Now, we have to find the derivative of \[{{e}^{3}}\].
We can observe that in the expression \[{{e}^{3}}\] there is no any x and hence, \[{{e}^{3}}\] is termed as a constant. Even though it may not look like a constant such as 4, -7, or \[-\dfrac{3}{5}\] , \[{{e}^{3}}\] still has a calculable value that never changes. So that, we say that \[{{e}^{3}}\] is a constant.
Also by the basic rule of derivative we know that the derivative of a constant is zero that is \[\dfrac{d}{dx}\left( c \right)=0\] where \[c\] is a constant.
Thus now as, \[{{e}^{3}}\] is a constant and derivative of a constant is zero we can write
\[\Rightarrow \dfrac{d}{dx}\left( {{e}^{3}} \right)=0\]
Hence, the derivative of \[{{e}^{3}}\] is zero.

Note: In this type of question students may make mistakes in finding the derivative as the given function is an exponential function. Students have to take care that though the given function is an exponential function its power is a number only and no any x is present in that and hence it is a constant term.