How do you find the derivative of arcsinx?

to find the derivative, we can first make this easier to visualise. Say a second variable, y, is included to make this become y = arcsinx. now if we sin both sides, we get siny = x. we already know the derivative of siny is cosy, but of course we are trying to find d/dx. if we simply interchange siny with cosy we are actually finding d/dy. there are 2 ways to go from this point. we can use the "chain rule", which states that d/dy * dy/dx = d/dx. as we know that d/dy siny = cosy, we now get d/dx siny = cosy X dy/dx. doing the same to both sides, d/dx x = 1. we now have cosy dy/dx = 1, giving us dy/dx = 1/cosy. however we do not want our added variable to be included in our answer, so we need to get rid of the cosy and replace it with a function of xs. How can we do this? we can use the substitution sin2y + cos2y = 1. as x = siny from before, this becomes x2 + cos2y = 1. rearranging this gives cosy = (1-x2)1/2 and d/dx arcsinx = 1/(1-x2)1/2.

TG
Answered by Thomas G. Further Mathematics tutor

3568 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the set of values of x for which (x+4) > 2/(x+3)


Integrate ln(x) with respect to x.


A particle is undergoing circular motion in a horizontal circle, that lies within the smooth surface of a hemispherical bowl of radius 4r. Find the distance OC (explained in diagram) if the angular acceleration of the particle is equal to root (3g/8r).


Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0


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