How do you find the second derivative of #y=cos(x^2)# ?

1 Answer
mason m
Nov 23, 2015

#-2sin(x^2)-4x^2cos(x^2)#

Explanation:

This will require the chain rule. Recall that #d/dx[cos(u)]=-u'sin(u)#.

#y'=-d/dx[x^2]sin(x^2)#
#y'=-2xsin(x^2)#

To find the second derivative, we must use the product rule.

#y''=sin(x^2)d/dx[-2x]+(-2x)d/dx[sin(x^2)]#
#y''=-2sin(x^2)-2xcos(x^2)*d/dx[x^2]#
#y''=-2sin(x^2)-2xcos(x^2)*2x#
#y''=-2sin(x^2)-4x^2cos(x^2)#

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