How do you find the derivative of #3arccos(x/2) #?

1 Answer
Aug 4, 2016

Answer:

#dy/dx=-3/sqrt(4-x^2)#

Explanation:

#y=3cos^-1(x/2)#

#x=2 cos (y/3)#

Differentiate x with respect to y

#dx/dy=-2 sin(y/3).(1/3)#

#dx/dy=-(2/3) sin(y/3)#

We Need to find #dy/dx#
#dy/dx =-3/(2sin(y/3))#

#y/3=cos^-1(x/2)#
#dy/dx=-3/(2sin(cos^-1(x/2))#
#dy/dx=-3/(2sin (sin^-1((sqrt(4-x^2))/2))#
#dy/dx=-3/sqrt(4-x^2)#