$$(x^{4})^{5}\times x^{-\frac{1}{2}}$$
$\frac{39x^{\frac{37}{2}}}{2}$
$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{20}x^{-\frac{1}{2}})$$
$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{39}{2}})$$
$$\frac{39}{2}x^{\frac{39}{2}-1}$$
$$\frac{39}{2}x^{\frac{37}{2}}$$
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$x^{\frac{39}{2}}$
