Given that x=ln(t) and y=4t^3,a) find an expression for dy/dx, b)and the value of t when d2y/dx2 =0.48. Give your answer to 2 decimal place.

a) Firstly, differentiate x and y with respect to t. 

Giving you dx/dt = 1/t       and dy/dt = 12t2

dy/dx is found using the chain rule:

dy/dx = dy/dt x dt/dx = 12t3

b) You will need to differentiate dy/dx again with respect to t, to do this:

d2y/dx2=36t2 x dt/dx = 36t3

36t3=0.48

t=(0.48/36)1/3

t=0.24

SW
Answered by Sara W. Maths tutor

3301 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y = lnx + 4x^2 + 3e^4x with respect to x


A ball is projected at an angle b from the horizontal. With initial velocity V the ball leaves the ground at point O and hits the ground at point A. If Vcos(b) = 6u and Vsin(b) = 2.5u, how long does the ball take to travel between O and A.


Integrate: xe^x


Find the antiderivative of the function f(x)=(6^x)+1


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning