Given that f(x) = 1/x - sqrt(x) + 3. Find f'(1).

We are given that f(x) = 1/x - sqrt(x) + 3. Here, f(x) represents a function. A function is a relation or expression involving one or more variables. We are able to differentiate f(x) in order to find the gradient, f'(x), at a particular point on the graph. So the purpose of this question is to find the gradient of f(x) at x=1.
In order to differentiate quadratics, we use the typical formula where y=axb and dy/dx=abxb-1. With this information we are now able to differentiate f(x). To make f(x) simpler we write, f(x) = x-1 - x1/2 + 3. Using the formula for differentiation above, we deduce that f'(x) = -x-2 - (1/2)x-1/2. To conclude, we simply substitute x=1 into our formula for f'(x) and we obtain f'(1)= -3/2.

Answered by Maths tutor

6963 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is differentation and how does it work?


A particle, P, moves along the x-axis. At time t seconds, t > 0, the displacement, is given by x=1/2t^2(t ^2−2t+1).


Differentiate y = 2xln(x)


The first term of an arithmetic series is a and the common difference is d. The 12th term is 66.5 and the 19th term is 98. Write down two equations in a and d then solve these simultaneous equations to find a and d.


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