Supposing y = arcsin(x), find dy/dx

Suppose:
y = arcsin(x)
Then, x = sin(y)
And, dx/dy = cos(y) ----- (1)
Using: dy/dx = 1/(dx/dy);
Thus 1 becomes: dy/dx = 1/cos(y) ------ (2)
Using: sin^2(y) + cos^2(y) = 1;
We can rearrange 2 to: dy/dx = 1/sqrt(1 - sin^2(y))
Therefore dy/dx = 1/(sqrt(1 - x^2)

Answered by James N. Maths tutor

6033 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y = (3x^2 + 1)^2


Express x^2-4x+9 in the form (x-p)^2+q where p and q are integers


Given that y=sin2x(3x-1)^4, find dy/dx


y = 4x/(x^2+5). a) Find dy/dx, writing your answer as a single fraction in its simplest form. b) Hence find the set of values of x for which 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