Find the Total Differential of the Function $$z = - \frac { 1 } { x ^ { 5 } + y ^ { 10 } }$$

question 124

Multiple Choice

Find the total differential of the function $$z = - \frac { 1 } { x ^ { 5 } + y ^ { 10 } }$$

• A)\(d z = \frac { x ^ { 6 } } { \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d x + \frac { y ^ { 11 } } { \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d y\)
• B)\(d z = \frac { x ^ { 6 } } { 6 \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d x + \frac { y ^ { 11 } } { 11 \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d y\)
• C)\(d z = \frac { 5 x ^ { 4 } } { x ^ { 5 } + y ^ { 10 } } d x + \frac { 10 y ^ { 9 } } { x ^ { 5 } + y ^ { 10 } } d y\)
• D)\(d z = \frac { 5 x ^ { 4 } } { \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d x + \frac { 10 y ^ { 9 } } { \left( x ^ { 5 } + y ^ { 10 } \right) ^ { 2 } } d y\)
• E)\(d z = \frac { x ^ { 6 } } { 6 \left( x ^ { 5 } + y ^ { 10 } \right) } d x + \frac { y ^ { 11 } } { 11 \left( x ^ { 5 } + y ^ { 10 } \right) } d y\)

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