Question

Translate expressions written in Leibniz notation to “prime” notation, and vice versa.

$\frac{d}{dx}\left(\frac{d}{dx}\left(x^2\right)\right)$

Short answer

$\frac{d}{dx}\left(\frac{d}{dx}\left(x^2\right)\right)=f^{\text{'}\text{'}}\left(x^2\right)$

Step-by-step solution

Given Information

The given expression is$\frac{d}{dx}\left(\frac{d}{dx}\left(x^2\right)\right)$

Simplification

$\frac{d}{dx}\left(\frac{d}{dx}\left(x^2\right)\right)$is written in Leibnitz notation.

Let $f=x^2$

It means differentiation of function $x^2$with respect to$x$.

In prime notation, it is written as $f^{\text{'}\text{'}}\left(x^2\right)$