How do you find the derivative of $y = cos 2 x$ $y = cos 2x$ ?

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Answer 1 · 2016-01-05T21:21:43

$\frac{d y}{d x} = - 2 sin 2 x$ $dy/dx = -2sin2x$

what we have here is a function 2x inside another function cos .

This is known as a function of a function.

If we differentiate cosx we get - sinx

when we differentiate cos2x we get - sin2x but then have to differentiate 2x.

This can be written as y = cos2x

$\Rightarrow \frac{d y}{d x} = - sin 2 x . \frac{d}{d x} (2 x) = - sin 2 x . 2$ $rArr dy/dx = - sin2x . d/dx (2x )= - sin2x . 2$

$\Rightarrow \frac{d y}{d x} = - 2 sin 2 x$ $rArr dy/dx = -2sin2x$

How do you find the derivative of y = cos 2xy=cos2xy = cos 2x?