`y = cos(x^2)` Find y' and y''

Textbook Question

Chapter 3, 3.4 - Problem 47 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`dy/dx=-(sin(x^2))*(2x)`

` `y'= -2x*sin(x^2)

Derivative of the product of a function can be found by

d/dx(uv) = u*dv/dx +v*du/dx

y" = `-2(x*d/dxsin(x^2) + (sin(x^2))*d/dx(x))`

`y'' = -2(x*2x*cos(x^2) +sin(x^2)`

`y'' = -2(2x^2*cos(x^2) +sin(x^2)`

`y'' = -4x^2*cos(x^2) -2sin(x^2) `

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