$$(81 \times 125 \times { 5 }^{ 5 } \times { T }^{ 8 } ) \div { 15 }^{ 4 } \times { T }^{ 4 }$$
$625T^{12}$
$$\frac{10125\times 5^{5}T^{8}}{15^{4}}T^{4}$$
$$\frac{10125\times 3125T^{8}}{15^{4}}T^{4}$$
$$\frac{31640625T^{8}}{15^{4}}T^{4}$$
$$\frac{31640625T^{8}}{50625}T^{4}$$
$$625T^{8}T^{4}$$
$$625T^{12}$$
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$7500T^{11}$
$$\frac{\mathrm{d}}{\mathrm{d}T}(\frac{10125\times 5^{5}T^{8}}{15^{4}}T^{4})$$
$$\frac{\mathrm{d}}{\mathrm{d}T}(\frac{10125\times 3125T^{8}}{15^{4}}T^{4})$$
$$\frac{\mathrm{d}}{\mathrm{d}T}(\frac{31640625T^{8}}{15^{4}}T^{4})$$
$$\frac{\mathrm{d}}{\mathrm{d}T}(\frac{31640625T^{8}}{50625}T^{4})$$
$$\frac{\mathrm{d}}{\mathrm{d}T}(625T^{8}T^{4})$$
$$\frac{\mathrm{d}}{\mathrm{d}T}(625T^{12})$$
$$12\times 625T^{12-1}$$
$$7500T^{12-1}$$
$$7500T^{11}$$
