How to differentiate y=sin(x°), where x is the angle in degrees rather than radians.

When you want to differentiate the sine function (sin(x)) with respect to an angle measured in degrees, you should take into account that most calculus operations are typically performed with angles measured in radians, not degrees. The derivative of sin(x) with respect to radians is well-known and is equal to cos(x).

However, if you're specifically working with degrees, you need to adjust for the difference between degrees and radians when finding the derivative. The conversion factor between degrees and radians is that π radians is equivalent to 180 degrees.

So, when you want to find the derivative of sin(x) with respect to degrees, you'll need to apply the chain rule and convert degrees to radians. The chain rule states that if you have a function y = sin(u), and u is a function of x, then the derivative dy/dx is given by:

dy/dx = (dy/du) * (du/dx)

In this case, u = x degrees, and we need to convert x from degrees to radians, which can be done using the conversion factor π radians = 180 degrees. So, du/dx is π/180.

Now, we know that the derivative of sin(u) with respect to u (dy/du) is cos(u). So, putting it all together:

dy/dx = (dy/du) * (du/dx) = cos(u) * (π/180)

Substituting u = x degrees:

dy/dx = cos(x degrees) * (π/180)

This is the derivative of sin(x) with respect to x when x is measured in degrees. Remember that you'll need to convert back to degrees if you're working with degree measurements.