Question

What is the derivative of ${e^{ax}}$ ?

Answer 1

Hint : The derivative of a function is calculated by finding the differentiation of a function.In this case our given function is an exponential function which means that it has a term $e$ in it. The differentiation of an exponential function is done by using the standard formula for differentiation of exponential function, the formula is as follows,
$\dfrac{d}{{dx}}({e^{ax}}) = a{e^{ax}}$
And we will get our final answer very easily.

Complete step by step solution:
The given question asks us to find the derivative of the given function which means that we have to find out its differentiation with respect to the variable $x$ . The given function is an exponential function with the base $e$
We will differentiation using the standard formula for exactly this type of question which is written as,
$\dfrac{d}{{dx}}({e^{ax}}) = a{e^{ax}}$
As we can see this is what we in fact require for the function therefore we get our answer in only a single step, that step is the above standard formula. Thus derivative of the given function, ${e^{ax}}$ is $a{e^{ax}}$ .
So, the correct answer is “ $a{e^{ax}}$ ”.

Note : The differentiation of a constant or an independent variable which is not the differentiating variable is always zero. The differentiation of a number or an independent variable other than the differentiating variable which is in effect as the coefficient of the function of the given variable is just multiplied and is not zero . The independent variable other than the differentiating variable in the above given function which we had to calculate the differentiation for is the constant $a$ .