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Mixed Differentiation

Mixed Differentiation Problems 1

We assume that you have mastered these methods already.

These problems can all be solved using one or more of the rules in combination.

The next example shows the application of the Chain Rule differentiating one function at each step. Not surprisingly the end result is the same.

Example

Find the derivative of y = sin(ln(5x2 − 2x))

This way of writing down the steps can be handy when you need to deal with using the Chain Rule more than once or when you need to use a mixture of methods.

Exercises

For each function obtain the derivative.

  1. y = 12x5 + 3x4 + 7x3 + x2 − 9x + 6
  2. y = sin (5x3 + 2x)  
  3. y = x2sin 2x
  4. y = x4(sin x3 − cos x2)
  5. y = e3x − 2

Check first 5 answers (this will open a new window)

  1. y = 4xe2x − 9x
  2. y =  cos x over x
  3. y =  x over cos x
  4. y =  ln sin 5x3
  5. y =  e to the power of the square root of ( 2x - 17 )

Check next 5 answers (this will open a new window)

  1. y = 4xe−5x
  2. y = 10(cos x) −10x
  3. y = 4ex(1 + ln x)(sin x)
  4. y = exln (5x3 + x2)
  5. y = (2x  plus 3) over (x plus 1)

Check next 5 answers (this will open a new window)

  1. y = (cos x)(1 − sin2x)
  2. y = 5xe2 + 5x
  3. y = cosec 3x
  4. y = ln (4e3x)
  5. y =x squared divided by the natural log of ( 1 minus 4 (x squared))

 Check last answers (this will open a new window)

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