$$f^{9}\div(f^{6})^{2}\times f^{6}=$$
$f^{3}$
$$\frac{f^{9}}{f^{12}}f^{6}$$
$$\frac{1}{f^{3}}f^{6}$$
$$\frac{f^{6}}{f^{3}}$$
$$f^{3}$$
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$3f^{2}$
$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f^{9}}{f^{12}}f^{6})$$
$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{1}{f^{3}}f^{6})$$
$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f^{6}}{f^{3}})$$
$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{3})$$
$$3f^{3-1}$$
$$3f^{2}$$
