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)

JN
Answered by James N. Maths tutor

6283 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the equation 2cos2(x) + 3sin(x) = 3, where 0<x<=π


Integrate ln(x)


Points P and Q are situated at coordinates (5,2) and (-7,8) respectively. Find a) The coordinates of the midpoint M of the line PQ [2 marks] b) The equation of the normal of the line PQ passing through the midpoint M [3 marks]


Show that arctan(x)+e^x+x^3=0 has a unique solution.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences