Solve 1^{2}+2^{2}+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^2+16^2+17^2+18^2

$$1 ^ { 2 } + 2 ^ { 2 } + 5 ^ { 2 } + 4 ^ { 2 } + 5 ^ { 2 } + 6 ^ { 2 } + 7 ^ { 2 } + 8 ^ { 2 } + 9 ^ { 2 } + 10 ^ { 2 } + 11 ^ { 2 } + 12 ^ { 2 } + B ^ { 2 } + 14 ^ { 2 } + 15 ^ { 2 } + 16 ^ { 2 } + 17 ^ { 2 } + 18 ^ { 2 }$$

Evaluate

$$B^{2}+1956$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$1+2^{2}+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1+4+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 1 and 4 to get 5.

$$5+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 5 to the power of 2 and get 25.

$$5+25+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 5 and 25 to get 30.

$$30+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 4 to the power of 2 and get 16.

$$30+16+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 30 and 16 to get 46.

$$46+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 5 to the power of 2 and get 25.

$$46+25+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 46 and 25 to get 71.

$$71+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 6 to the power of 2 and get 36.

$$71+36+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 71 and 36 to get 107.

$$107+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 7 to the power of 2 and get 49.

$$107+49+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 107 and 49 to get 156.

$$156+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 8 to the power of 2 and get 64.

$$156+64+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 156 and 64 to get 220.

$$220+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 9 to the power of 2 and get 81.

$$220+81+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 220 and 81 to get 301.

$$301+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 10 to the power of 2 and get 100.

$$301+100+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 301 and 100 to get 401.

$$401+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 11 to the power of 2 and get 121.

$$401+121+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 401 and 121 to get 522.

$$522+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 12 to the power of 2 and get 144.

$$522+144+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 522 and 144 to get 666.

$$666+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 14 to the power of 2 and get 196.

$$666+B^{2}+196+15^{2}+16^{2}+17^{2}+18^{2}$$

Add 666 and 196 to get 862.

$$862+B^{2}+15^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 15 to the power of 2 and get 225.

$$862+B^{2}+225+16^{2}+17^{2}+18^{2}$$

Add 862 and 225 to get 1087.

$$1087+B^{2}+16^{2}+17^{2}+18^{2}$$

Calculate 16 to the power of 2 and get 256.

$$1087+B^{2}+256+17^{2}+18^{2}$$

Add 1087 and 256 to get 1343.

$$1343+B^{2}+17^{2}+18^{2}$$

Calculate 17 to the power of 2 and get 289.

$$1343+B^{2}+289+18^{2}$$

Add 1343 and 289 to get 1632.

$$1632+B^{2}+18^{2}$$

Calculate 18 to the power of 2 and get 324.

$$1632+B^{2}+324$$

Add 1632 and 324 to get 1956.

$$1956+B^{2}$$

Differentiate w.r.t. B

$$2B$$

Steps Using Derivative Rule for Sum

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1+2^{2}+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1+4+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}B}(5+5^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}B}(5+25+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 5 and 25 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}B}(30+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}B}(30+16+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 30 and 16 to get 46.

$$\frac{\mathrm{d}}{\mathrm{d}B}(46+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}B}(46+25+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 46 and 25 to get 71.

$$\frac{\mathrm{d}}{\mathrm{d}B}(71+6^{2}+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\mathrm{d}}{\mathrm{d}B}(71+36+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 71 and 36 to get 107.

$$\frac{\mathrm{d}}{\mathrm{d}B}(107+7^{2}+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\mathrm{d}}{\mathrm{d}B}(107+49+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 107 and 49 to get 156.

$$\frac{\mathrm{d}}{\mathrm{d}B}(156+8^{2}+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}B}(156+64+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 156 and 64 to get 220.

$$\frac{\mathrm{d}}{\mathrm{d}B}(220+9^{2}+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}B}(220+81+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 220 and 81 to get 301.

$$\frac{\mathrm{d}}{\mathrm{d}B}(301+10^{2}+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}B}(301+100+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 301 and 100 to get 401.

$$\frac{\mathrm{d}}{\mathrm{d}B}(401+11^{2}+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 11 to the power of 2 and get 121.

$$\frac{\mathrm{d}}{\mathrm{d}B}(401+121+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 401 and 121 to get 522.

$$\frac{\mathrm{d}}{\mathrm{d}B}(522+12^{2}+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 12 to the power of 2 and get 144.

$$\frac{\mathrm{d}}{\mathrm{d}B}(522+144+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 522 and 144 to get 666.

$$\frac{\mathrm{d}}{\mathrm{d}B}(666+B^{2}+14^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 14 to the power of 2 and get 196.

$$\frac{\mathrm{d}}{\mathrm{d}B}(666+B^{2}+196+15^{2}+16^{2}+17^{2}+18^{2})$$

Add 666 and 196 to get 862.

$$\frac{\mathrm{d}}{\mathrm{d}B}(862+B^{2}+15^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 15 to the power of 2 and get 225.

$$\frac{\mathrm{d}}{\mathrm{d}B}(862+B^{2}+225+16^{2}+17^{2}+18^{2})$$

Add 862 and 225 to get 1087.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1087+B^{2}+16^{2}+17^{2}+18^{2})$$

Calculate 16 to the power of 2 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1087+B^{2}+256+17^{2}+18^{2})$$

Add 1087 and 256 to get 1343.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1343+B^{2}+17^{2}+18^{2})$$

Calculate 17 to the power of 2 and get 289.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1343+B^{2}+289+18^{2})$$

Add 1343 and 289 to get 1632.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1632+B^{2}+18^{2})$$

Calculate 18 to the power of 2 and get 324.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1632+B^{2}+324)$$

Add 1632 and 324 to get 1956.

$$\frac{\mathrm{d}}{\mathrm{d}B}(1956+B^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2B^{2-1}$$

Subtract 1 from 2.

$$2B^{1}$$

For any term t, t^{1}=t.

$$2B$$