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

question 58

Multiple Choice

Write the function in the form y = f(u) and u = g(x) . Then find dy/dx as a function of x.
- $$y = \cot ( 10 x - 5 )$$

• A) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - 10 \cot ( 10 x - 5 ) \csc ( 10 x - 5 )\)
• B) \(y = 10 u - 5 ; u = \cot x ; \frac { d y } { d x } = - 10 \cot x \csc ^ { 2 } x\)
• C) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - 10 \csc ^ { 2 } ( 10 x - 5 )\)
• D) \(y = \cot u ; u = 10 x - 5 ; \frac { d y } { d x } = - \csc ^ { 2 } ( 10 x - 5 )\)

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