For f(x) = (3x+4)^(-2), find f'(x) and f''(x) and hence write down the Maclaurin series up to and including the term in x^2.

f'(x)=-2(3x+4)^(-3) * 3 = -6(3x+4)^(-3);
f''(x)= 18(3x+4)^(-4) * 3 = 54(3x+4)^(-4);
both found by using the chain rule for differentiation.

Then Maclaurin series up to x^2 is: f(x)=f(0)+f'(0)x+1/2 f''(0)x^2;
Which here gives f(x)=4^(-2) - 6*(4)^(-3) x + 27*(4)^(-4) x^2.

Related Further Mathematics A Level answers

All answers ▸

How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?


Split x^4/[(x^2+4)*(x-2)^2] into partial fractions and hence differentiate it


The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2


Find the square roots of 2 + isqrt(5)


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