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DifferentiationVariable power functions aka Logarithmic DifferentiationYou need to have mastered the Chain Rule before you start logarithmic differentiation. When a function contains another function as a power, so the power is variable, we cannot use our previous methods. Simple examples include 5x, 2x−3x and (x2 + 3x − 24)3 − 2x The problem is easily solved if we first apply the natural log function to both sides and use the rules we learnt before. Remember: Hit it with a log! ExampleDifferentiate y = 8x Now a more complicated expression. Differentiate y = f(x) = x2x. The method is summarised:
More examples (this will open a new window) ExerciseFirst some simpler exercises to get you used to the method. ExerciseNow try your hand at some more challenging exercises. ExerciseThe previous exercises have a more limited scope than this exercise. Differentiate these variable power functions:
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