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

1 Answer
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)