# sir, my name is Akshaya and i have a doubt in one of the example sum - Given X=a2b1/3 / c3.find the error percentage of X if the percentage of errors in a,b,c are 2,4, and 5 respectively. sir please clarify my doubt.

Given that X= a2 b1/3 /c3
Applying logarithms on both sides,
log x= 2loga+(1/3)logb+3logc   ( In concept of errors errors should be added so minus sign is taken as plus)
Differentiating both sides;
dX/X= 2(d(a)/a) + (1/3)(d(b)/b)+3(d(c)/c)
multiplying with 100 on both sides we can consider as percentage error in a,b and c respectively.
Substituting the given values,
(dX/X)*100= 2(2)+(1/3)*4+3*5
= 61/3 %= 20.33%

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