Question

What is the derivative of $\dfrac{4}{x}$ ?

Answer 1

Hint : The derivative of a function is known as the differentiation of that particular function. We know that differentiation can be done by using the standard formula of the question of the given type. The question is given as, $\dfrac{4}{x}$ the standard formula that can be used for solving differentiation of this type of questions is given by
$\dfrac{d}{{dx}}{x^n} = n{x^{n - 1}}$
The question given here might not look like it belongs to this form but it can be converted to this form as the power of $x$ in the given function is $- 1$ because numbers in reciprocal get a negative sign before their index.
The function will be differentiated by taking the power as $- 1$ .

Complete step by step solution:
We have to differentiate the given function . The function is :
$\dfrac{4}{x}$
Which can be rewritten as,
$4{x^{ - 1}}$ as the power in a reciprocal get a negative sign when written in the numerator.
The given function will now be differentiated by using the formula,
$\dfrac{d}{{dx}}{x^n} = n{x^{n - 1}}$
Now differentiating the function we get,
$\dfrac{d}{{dx}}4{x^{ - 1}} = - 4{x^{ - 2}}$
Which on further simplification becomes,
$- \dfrac{4}{{{x^2}}}$
Which is the required answer for the given function.
So, the correct answer is “ $- \dfrac{4}{{{x^2}}}$ ”.

Note : Always keep these points in mind while finding out the derivative of any question.
The differentiation of a constant is always zero . ie The differentiation of a number like $1,2,3$ and other variables in the question other than the differentiation variable is always zero.
The most common formula for differentiation of a variable with an index is given by ,
$\dfrac{d}{{dx}}{x^n} = n{x^{n - 1}}$ where $n$ is the power of the given variable.