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Calculus, 2ADV C1 EQ-Bank 4 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
\(y\) \(=n x^{2n+1}\)  
\(y^{′}\) \(=(2 n+1) n x^{2n+1-1}\)  
  \(=(2 n+1) n x^{2 n}\)  

 
\(\Rightarrow C\)

Filed Under: Standard Differentiation, Standard Differentiation Tagged With: Band 4, smc-1069-30-Basic Differentiation, smc-6436-30-Basic Differentiation

Calculus, 2ADV C1 2004 HSC 1b

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

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`4x^3 – 5x^(-2)`

Show Worked Solution
`y` `= x^4 + 5x^(-1)`
`dy/dx`  `= 4x^3 – 5x^(-2)`

Filed Under: Standard / 1st Principles, Standard Differentiation, Standard Differentiation Tagged With: Band 3, smc-1069-30-Basic Differentiation, smc-6436-30-Basic Differentiation

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