Question

If y=(sin x)cos x then dy/dx=?​

Answer 1

y' = sinx (-sinx) + cosx ( cosx)

=

$cos ^{2} x - \sin ^{2} x$

= cos2x

Answer 2

hey mate

given here:

y= sin x (cos x)

find here:

dy/dx= ?

solution :

y= sin x (cos x)

differentiate with respect to x.

we get,

dy/dX= d/dx[ sin x (cos x)]

using here chain rule :

if y= pq

so,

dy/dx= p( dq/dx)+q(dp/dx)

now,

dy/dX= d/dx[ sin x (cos x)]

= sin x [ d/dx(cos x ) ] + cos x [ d/dx(sin x)]

= sin x (- sin x ) + cos x ( cos x)

= cos ²x - sin ²x

we know that ,

cos 2x = cos ²x - sin ²x

so,

dy/dx = cos 2x.

I hopes its helps u.

@Abhi.❤❤

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