How do you differentiate $cos (x^{2} + 5)$ $cos(x^2+5)$ ?

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Answer 1 · 2016-12-06T15:10:36

The answer is $= - 2 x sin (x^{2} + 5)$ $=-2xsin(x^2+5)$

You use chain differentiation

If $y = cos u (x)$ $y=cosu(x)$

$dy/dx=-sin(u(x))*u'(x)$

Here, $u(x)=x^2+5$

$u'(x)=2x$

So,

$(cos(x^2+5))'=-sin(x^2+5)*2x$

How do you differentiate cos(x^2+5)cos(x2+5)cos(x^2+5)?