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

5950 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the line that is perpendicular to the line 3x+5y=7 and passes through point (-2,-3) in the form px+qy+r=0


Show that the curve y =f(x) has exactly two turning points, where f(x)= x^3 - 3x^2 - 24x - 28


A level Maths question - The graph of y=2sin(2x)+1 is rotated 360 degrees about the x-axis to form a solid. Find the volume enclosed by the curve, the co-ordinate axes and the line x=pi/2


Find the integral I of e^(2x)*cos*(x), with respect to x


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