Solve 2001+{left(2000^2right)}^{{left(2^2right)}^{{left(2^2right)}^{{left(2^2right)}^{{left({2}^{2}right)}^{{left({2}^{2}right)}^{{left({2}^{2}right)}^{2{2}^{2}%{left(7{7}^{2}{7}^2{left({7}^2right)}^4x2right)}^2}}}}}}}

$$2001+ { \left( { 2000 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ { \left( { 2 }^{ 2 } \right) }^{ 2 { 2 }^{ 2 } \% { \left(7 { 7 }^{ 2 } { 7 }^{ 2 } { \left( { 7 }^{ 2 } \right) }^{ 4x2 } \right) }^{ 2 } } } } } } } }$$

Evaluate

$$2000^{2^{2^{2^{2^{2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+1}+1}+1}+1}}+2001$$

Differentiate w.r.t. x_2

$$\frac{18078415936\ln(7)\ln(2000)\ln(2)^{6}\times 7^{16x_{2}}\times 2^{2^{2^{2^{2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+1}+1}+1}+2^{2^{2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+1}+1}+2^{2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+1}+2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+\frac{1129900996\times 7^{16x_{2}}}{25}+6}\times 2000^{2^{2^{2^{2^{2^{2^{\frac{1129900996\times 7^{16x_{2}}}{25}+1}+1}+1}+1}+1}+1}}}{25}$$