Question

If y = Sinx into Cosx then dy / dx is equal to​

Answer 1

Answer:

dy/dx = cos 2x

Explanation:

Given,

y = sin x . cos x

Differentiate with respect to x,

we get,

dy/dx = d/dx (sin x cos x)

We apply chain rule here,

if y = pq, then

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

⇒ dy/dx = d/dx (sin x cos x)

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

⇒ dy/dx = sin x (- sin x ) + cos x ( cos x)

⇒ dy/dx = cos ²x - sin ²x

we know that ,

cos 2x = cos ²x - sin ²x

so,

dy/dx = cos 2x.