Differentiate the functions given in Exercises 1 to 11 w.r.t. x.1. cos x . cos 2x . cos 3x

To differentiate the function cos(x) . cos(2x) . cos(3x) with respect to x, we will use the product rule of differentiation which states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Let's denote: f(x) = cos(x) g(x) = cos(2x) h(x) = cos(3x)

The derivative of the function will be:

f'(x)g(x)h(x) + f(x)g'(x)h(x) + f(x)g(x)h'(x)

Now, we find the derivatives of f, g, and h:

f'(x) = -sin(x) g'(x) = -2sin(2x) h'(x) = -3sin(3x)

Substitute these values back into our equation:

= -sin(x)cos(2x)cos(3x) - 2cos(x)sin(2x)cos(3x) - 3cos(x)cos(2x)sin(3x)

So, the derivative of cos(x) . cos(2x) . cos(3x) with respect to x is -sin(x)cos(2x)cos(3x) - 2cos(x)sin(2x)cos(3x) - 3cos(x)cos(2x)sin(3x).