How do you differentiate $cos(x^4)$ ?

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Answer 1 · 2016-09-05T12:33:50

$- 4 x^(7)$

We have: $cos(x^(4))$

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

Let $u = x^(4) => u' = 4 x^(3)$ and $v = cos(u) => v' = - sin(u)$ :

$=> (d) / (dx) (cos(x^(4))) = 4 x^(3) cdot - sin(u)$

$=> (d) / (dx) (cos(x^(4))) = - 4 u x^(3)$

We can now replace $u$ with $x^(4)$ :

$=> (d) / (dx) (cos(x^(4))) = - 4 (x^(4)) x^(3)$

$=> (d) / (dx) (cos(x^(4))) = - 4 x^(4 + 3)$

$=> (d) / (dx) (cos(x^(4))) = - 4 x^(7)$

How do you differentiate cos(x^4)cos(x^4)?