How do you differentiate f (x) =cos2x?

We have to differeniate f(x) = cos2x

Solution

Given

f(x) = cos2x

We can express the given equation as

f(x) = (cos x)2

Let us assume u=cos x

On differeinating we get

du/dx= -sin x

Now let us consider y=u2

On differeinating we get

dy/du=2u

dy/dx= 2u (-sin x)

Substituting u back in terms of x we get,

dy/dx= – 2 sinx cos x

We know from the trigonemretric identity that

sin 2x= 2 sin x cos x

substituting the identity in the above differentiated equation we get

dy/dx= – sin 2x

Answer

Differeniation of f(x) = cos2x= dy/dx= – sin 2x

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