Find the gradient of the curve y = x^2(ln(x)) at x = e

We'll need to use the product rule.

Let's take u = x^2 -> du/dx = 2x, and v = ln(x) -> dv/dx = 1/x

Then dy/dx = x^2(1/x) + 2xln(x) = x + 2xln(x)

Substituting our x value gives (dy/dx)|(x = e) = e + 2eln(e) = 3e

Answered by Charlie R. Maths tutor

4657 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

When Integrating by parts, how do you know which part to make "u" and "dv/dx"?


A circle has equation: (x - 2)^2 + (y - 2)^2 = 16. It intersects the y-axis (y > 0) at point P and the x-axis (x < 0) at point Q. Find the equation of the line connecting P and Q and of the line perpendicular to PQ passing through the circle's centre.


Integrate 3x^2+cos(x) with respect to x


How do you multiply matrices together?


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