1.

The derivative of In(x + sin x) with respect to (x + cos x) is

A. \(\frac{{1 + \cos {\rm{x}}}}{{\left( {{\rm{x}} + \sin {\rm{x}}} \right)\left( {1 - \sin {\rm{x}}} \right)}}\)
B. \(\frac{{1 - \cos {\rm{x}}}}{{\left( {{\rm{x}} + \sin {\rm{x}}} \right)\left( {1 + \sin {\rm{x}}} \right)}}\)
C. \(\frac{{1 - \cos {\rm{x}}}}{{\left( {{\rm{x}} - \sin {\rm{x}}} \right)\left( {1 + \cos {\rm{x}}} \right)}}\)
D. \(\frac{{1 + \cos {\rm{x}}}}{{\left( {{\rm{x}} - \sin {\rm{x}}} \right)\left( {1 - \cos {\rm{x}}} \right)}}\)
Answer» B. \(\frac{{1 - \cos {\rm{x}}}}{{\left( {{\rm{x}} + \sin {\rm{x}}} \right)\left( {1 + \sin {\rm{x}}} \right)}}\)


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