Question

Find the derivative of:
y = cos^2(x) + cos(x^2)

Answer 1

y = (cos(x))^2 + cos(x^2)

//power rule for the cos(x). also you have to take the derivative of the inside of the cos(x)
y' = 2*(cos(x))*(-sin(x)) + d/dx(cos(x^2))

// now take the derivative of the second part of the sum. no power rule. just take derivative of the cos() and then the derivative of the inside.
y' = 2*(cos(x))*(-sin(x)) + (-sin(x^2))*(2x)

// so you can factor a 2 if you want.

Answer 2

Why would you have the first -sin(x)?

Answer 3

Shouldn't it just be -1? I'm lost.

Answer 4

you have to take the derivative of the cos(x) which is -sin(x)

Answer 5

Oh right... duh. Thank you so much!

Answer 6

yw