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sir, my name is Akshaya and i have a doubt in one of the example sum -

Given X=a^{2}b^{1/3} / c^{3.}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.

^{2}b

^{1/3}/c

^{3}

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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