Let y = x^x. Find dy/dx.
This question is suited to A2 maths students, particularly those who are doing further maths and may be looking for a challenge. In one question it tests the students ability to use implicit differentiation, the chain rule, the product rule, and log laws.Solution:We cannot simply multiply by the power and reduce it by 1 since our exponent is not a constant. We can take the natural logarithm of both sides, yielding log(y) = x log(x). We can then use implicit differentiation on the LHS and the product rule on the RHS to get (1/y) * dy/dx = log(x) + 1. We can then multiply through by y = xx to get our final form of dy/dx = xx(log(x) + 1). During a session these steps would be much more filled out - this is far easier to do with access to a whiteboard.
