Turunan pertama dari [tex]y = \frac{(4x^3 \sqrt{x} + x^{2} )^2}{x \sqrt{x}} [/tex]...

Ubah ke bentuk umum terlebih dahulu:
[tex]$\begin{align}y&=\frac{(4x^3\sqrt x+x^2)^2}{x\sqrt x}=\frac{(4x^{7/2}+x^2)^2}{x^{3/2}} \\ &=\frac{(4x^{7/2})^2+2(4x^{7/2})(x^2)+(x^2)^2}{x^{3/2}} \\ &=\frac{16x^7+8x^{11/2}+x^4}{x^{3/2}} \\ &=16x^{7-\frac32}+8x^{\frac{11}2-\frac32}+x^{4-\frac32} \\ &=16x^{11/2}+8x^4+x^{5/2}\end{align}[/tex]

Lakukan turunan menggunakan aturan pangkat:
[tex]\boxed{\frac d{dx}\ x^n=nx^{n-1}}[/tex]

Sehingga, diperoleh:
[tex]$\begin{align}y'&=16\times\left(\frac{11}2x^{9/2}\right)+8(4x^3)+\frac52x^{3/2} \\ &=88x^{9/2}+32x^3+\frac52x^{3/2} \\ &=88x^4\sqrt x+32x^3+\frac52x\sqrt x\end{align}[/tex]