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Calculus, 2ADV C1 EO-Bank 1 MC v1

The derivative of  \((n^2-1) x^{3n-2}\)  can be expressed as

  1. \(3(n-1)(n^2-1) x^{3n-2}\)
  2. \(3(n-1)(n^2-1) x^{3(n-1)}\)
  3. \((3n-2) (n^2-1) x^{3(n-1)}\)
  4. \((3n-2) (n^2-1) x^{3n-2}\)
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\(C\)

Show Worked Solution
\(y\) \(=(n^2-1) x^{3n-2}\)  
\(y^{′}\) \(=(3n-2) (n^2-1) x^{3n-2-1)}\)  
  \(=(3n-2) (n^2-1) x^{3(n-1)}\)  

 
\(\Rightarrow C\)

Calculus, 2ADV C1 EO-Bank 7

Differentiate  `2x(1-4x)^5`  with respect to `x`.   (2 marks)

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`y^{′}=2(1-4x)^4(1-24x)`

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`y=2x(1-4x)^5`

`text{Using the product and chain rules:}`

`y^{′}` `=2 xx (1-4x)^5-40x(1-4x)^4`  
  `=2(1-4x)^4(1-4x-20x)`  
  `=2(1-4x)^4(1-24x)`  

Calculus, 2ADV C1 EQ-Bank 1 MC

The derivative of  \(n x^{2n+1}\)  can be expressed as

  1. \(2 n^2 x^{2 n+1}\)
  2. \(2 n^2 x^{2 n}\)
  3. \((2 n+1) n x^{2 n}\)
  4. \((2 n+1) n x^{2 n+1}\)
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\(C\)

Show Worked Solution
\(y\) \(=n x^{2n+1}\)  
\(y^{′}\) \(=(2 n+1) n x^{2n+1-1}\)  
  \(=(2 n+1) n x^{2 n}\)  

 
\(\Rightarrow C\)