Find the second derivate d^2y/dx^2 when y = x^6 + sqrt(x).

Initially we find the first derivative of the function y = x6 + sqrt(x). We achieve this by multiplying each x term by the power it is raised to, then reducing the power by 1. Solution:
1) It helps to initially simplify the sqrt(x) term to x1/2 to give: y = x6 + x1/2
2) We can then determine the first derivative: dy/dx = 6x5+ 1/2x-1/2
To determine the second derivative we then take the first derivative and differentiate that function, repeating the prior steps:
3) d2y/dx2 = 30x4 + (-1/4)x-3/2
We can simplify the answer to give:
4) d2y/dx2 = 30
x4 -1/4
x-3/2
Simplifying fully gives:
5) d2y/dx2 = 30x4 - (1/(4x3/2))

Related Maths A Level answers

All answers ▸

Find the volume of revolution when the area B is rotated 2 pi radians about the x axis


Find the derivative of yx+5y-sin(y) = x


How would we evaluate (1/3)^-3/2 ?


How do I find a stationary point? And how do I determine whether it is a maximum or minimum point?


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences