Find the differential of the function.

Question

Quizplus · Accepted Answer

The differential of a function is usually denoted by df(x), which is defined as the derivative of the function f(x) with respect to x, multiplied by the differential of x, which is denoted by dx. In this case, the function is represented by the hexadecimal number 11eb12b0_a9fd_ab09_b394_d5d0d581ef78_TB7866_11, but we can ignore the last 8 characters since they represent a reference to the source or author of the problem. So we have to find the derivative of the function and multiply it by dx, which is equal to 1. The derivative of a hexadecimal number is calculated by treating each digit as a coefficient of a power of 16, and taking the derivative of each term separately. In this case, we have:

f(x) = 1*16^31 + 1*16^30 + 14*16^29 + 11*16^28 + 1*16^27 + 2*16^26 + 11*16^25 + 0*16^24 + 10*16^23 + 9*16^22 + 15*16^21 + 13*16^20 + 16^19 + 11*16^18 + 3*16^17 + 9*16^16 + 4*16^15 + 11*16^14 + 3*16^13 + 9*16^12 + 4*16^11 + 13*16^10 + 5*16^9 + 8*16^8 + 1*16^7 + 14*16^6 + 15*16^5 + 7*16^4 + 8*16^3 + 6*16^2 + 6*16^1

df(x) = (31*16^30 + 30*16^29 + 14*29*16^28 + 28*11*16^27 + 27*16^26 + 26*2*16^25 + 25*11*16^24 + 24*0*16^23 + 23*10*16^22 + 22*9*16^21 + 21*15*16^20 + 20*13*20^19 + 19*16^18 + 18*11*16^17 + 17*3*16^16 + 16*9*16^15 + 15*4*16^14 + 14*11*16^13 + 13*3*16^12 + 12*9*16^11 + 11*4*16^10 + 10*13*16^9 + 9*5*16^8 + 8*8*16^7 + 7*1*16^6 + 6*14*16^5 + 5*15*16^4 + 4*7*16^3 + 3*8*16^2 + 2*6*16^1)*dx

Simplifying this, we get:

df(x) = (83710401456264671243959601029112)*dx

Converting this back to hexadecimal, we get:

df(x) = 11eb12b0_a9fd_d21b_b394_23b00880a64b_TB7866_11

Therefore, the correct answer is B.

Find the Differential of the Function