y=(6x^9 +x^8)/(2x^4), work out the value of d^2y/dx^2 when x=0.5

The question can be represented by the notation d2y/dx2|x=0.5, meaning the second derivative of y with respect to x resolved at x=0.5. Since y is in the form f(x)/g(x), the quotient rule could be used, but it would be much easier to first simplify y to 3x5 + x4/2, using the index rules (xm/xn = xm-n). Once y is in this form we can easily differentiate both terms with respect to x twice, giving dy/dx = 15x4 + 2x3, and then d2y/dx2 = 60x3 + 6x2. At this point we can substitute in x=0.5, giving d2y/dx2|x=0.5 = 60(0.5)3 + 6(0.5)2 = 9.

OC
Answered by Oscar C. Further Mathematics tutor

4044 Views

See similar Further Mathematics GCSE tutors

Related Further Mathematics GCSE answers

All answers ▸

Express (7+ √5)/(3+√5) in the form a + b √5, where a and b are integers.


The circle c has equation x^2+ y ^2=1 . The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.


Work out 7/(2x^2) + 4/3x as a single fraction in its simplest form.


If the equation of a curve is x^2 + 9x + 8 = y, then differentiate it.


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