What is the derivative of $cos(x^2)$ ?

Question

1181 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-04T08:25:53

$- 2x sin(x^(2))$

We have: $cos(x^(2))$

This expression can be differentiated using the "chain rule".

Let $u = x^(2) => (d) / (dx) (u) = 2x$ and $v = cos(u) => (d) / (du) (cos(u)) = - sin(u)$ :

$=> (d) / (dx) (cos(x^(2)) = 2x cdot - sin(u)$

$=> (d) / (dx) (cos(x^(2)) = - 2x sin(u)$

We can now replace $u$ with $x^(2)$ :

$=> (d) / (dx) (cos(x^(2)) = - 2x sin(x^(2))$

What is the derivative of cos(x^2)cos(x^2)?