Question

Find d² y/d x² if y=sin (x) cos (x).

Answer 1

The second derivative of y with respect to x is -2sin(x)cos(x).

Step-by-step explanation:

To find the second derivative of y with respect to x, we need to differentiate twice.

Let's start with finding the first derivative:

y = sin(x)cos(x)

Using the product rule, we have: y' = (cos(x))(cos(x)) + (sin(x))(-sin(x)) = cos²(x) - sin²(x)

To find the second derivative, we differentiate y' again:

y'' = (-2sin(x)cos(x))'

Using the product rule, we have:

y'' = (cos²(x) - sin²(x))' = -2sin(x)cos(x)

So therefore the second derivative of y with respect to x is -2sin(x)cos(x).