What is the derivative of x^x

Firstly we should notice the similarities between this expression and expressions of the standard type ax. 

To deal with this type of expression, we take logarithms of both sides and then apply the usual rules of differentiation. Let's try that here:

1.) y = x 

take logs of both sides and use the multiplicative law of logarithms 

2.) log(y) = xlog(x)

now use the chain rule on the LHS and the product rule on the RHS

3.) dy/dx * 1/y = 1 + log(x)

now simply rearrange to find dy/dx

4.) dy/dx = xlog(x)*(1+log(x))

Answered by Daniel K. Maths tutor

3555 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate with respect to x: y=(6x^2-1)/2sqrt(x)


By first proving that sin2θ=2sinθcosθ, calculate ∫1+sinθcosθ dθ.


Is AB perpendicular to BC where A =(2,0,-1), B=(4,3,-6) and C = (9,3,-4)


Find the first three terms in the binomial expansion of (8-9x)^(2/3) in ascending powers of x


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy