Write the Function in the Form Y = F(u) and U

question 29

Multiple Choice

Write the function in the form y = f(u) and u = g(x) . Then find dy/dx as a function of x.
- $$y = \left( 5 x ^ { 2 } - \frac { 6 } { x } - x \right) ^ { 8 }$$

• A) \(y = u ^ { 8 } ; u = 5 x ^ { 2 } - \frac { 6 } { x } - x ; \frac { d y } { d x } = 8 \left( 5 x ^ { 2 } - \frac { 6 } { x } - x \right) ^ { 7 }\)
• B) \(y = u ^ { 8 } ; u = 5 x ^ { 2 } - \frac { 6 } { x } - x ; \frac { d y } { d x } = 8 \left( 10 x + \frac { 6 } { x ^ { 2 } } - 1 \right) ^ { 7 }\)
• C) \(y = 5 u ^ { 2 } - \frac { 6 } { u } - u ; u = x 8 ; \frac { d y } { d x } = 10 x + \frac { 6 } { x ^ { 8 } } - x ^ { 8 }\)
• D) \(y = u ^ { 8 } ; u = 5 x ^ { 2 } - \frac { 6 } { x } - x ; \frac { d y } { d x } = 8 \left( 5 x ^ { 2 } - \frac { 6 } { x } - x \right) ^ { 7 } \left( 10 x + \frac { 6 } { x ^ { 2 } } - 1 \right)\)

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