Question

$$\frac{ x }{ } \displaystyle\frac{d}{d \left( \displaystyle\frac{d}{d \left( \right) } \left( \right) x \right) } \left( \right)$$

Answer

$$x*d^2*f^4,*x,$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[xd\imath ffd\imath ff,x,\]
Regroup terms.
\[xddfff\imath \imath f,x,\]
Simplify  \(xddfff\imath \imath f\)  to  \(x{d}^{2}{f}^{3}\imath \imath f\).
\[x{d}^{2}{f}^{3}\imath \imath f,x,\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[x{d}^{2}{f}^{4}{\imath }^{2},x,\]
Use Square Rule: \({i}^{2}=-1\).
\[x{d}^{2}{f}^{4}\times -1\times ,x,\]
Simplify  \(x{d}^{2}{f}^{4}\times -1\times \)  to  \(x{d}^{2}{f}^{4}\).
\[x{d}^{2}{f}^{4},x,\]