


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 5^{x}, 2x^{−3x} and (x^{2} + 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 = 8^{x} Now a more complicated expression. Differentiate y = f(x) = x^{2x}. 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:
