Differentiate x^x
With the methods we know at A Level we cannot current differentiate xx in its current form. Therefore let y = xxTo turn it into a form we can differentiate we take the natural log of both sides. This gives ln(y) = ln(xx). Using the log rule (logab = bloga) we can then say ln(y) = xln(x). We can then differentiate implicitly to form a differential equation 1/y x dy/dx = ln(x) + 1. To find dy/dx we then simply multiply through by y to give...dy/dx = y(lnx + 1) = xx(lnx + 1)
Related Maths A Level answers
All answers ▸How can the y=sin(x) graph be manipulated?
Two particles, A and B, are moving directly towards each other on a straight line with speeds of 6 m/s and 8 m/s respectively. The mass of A is 3 kg, and the mass of B is 2 kg. They collide to form a single particle of speed "v" m/s. Find v.
What are complex and imaginary numbers and how are they different from normal (real) numbers?
Find 1 + (1 + (1 + (1 + (1 + ...)^-1)^-1)^-1)^-1