This function is known as differentiation of trigonometric function with use of calculus and various trigonometry rules.
Derivative of Cos Squared X
Derivative of any trigonometric function that is we have to differentiate the function one time. Here we have to find the derivative of Cos squared X. for this first we know the basic rules of differentiation. And also rules of trigonometry.
Derivative of Cos Squared X means first we write the function in (cosX)^2 , now we have to use chain rule . Take external term derivative from the function and then differentiate the internal term we get (2cosxsinx) with negative sign because one time differentiation of cos function is negative sine function.
Now by using trigonometry rule change the result means -2cosxsinx is replaced with -2sin2x. so finally we get derivative of cos squared x is( -2sin2x).
Derivative of Cos -1
Derivative of Cos-1 means we have to differentiate only cos function and cos-1 is a cos function only. So by differentiating that is derivative of cos-1 is sin-1 with negative sign. We have to differentiate only one time.
Derivative of Inverse Cos
For finding the derivative of inverse Cos we use inverse trigonometric rule and calculus rules. Inverse trigonometric function also called sometime as cyclometric function. They are inverse of trigonometric function with proper domains. These are also used as arcos, arcsin and etc.
Inverse laws are very restricted and we can’t go out of the domains. These are proper subsets of domains. Like if function y=square root of x then we write this function as y^2=x also. Similarly function y=arccos then we write this function as cosy=x also. And then differentiate the function.
Derivative of inverse Cos by differentiating we get 1/square root of (1-x^2).
d/dx (arcos) =1/square root of (1-x^2)
Derivative of Cos X Squared
Derivative of Cos X Squared, we write this function also as y=(Cosx)^2, now we differentiate one time this function with respect to x. Differentiate the external term we get 2 cosx now differentiate the internal term cosx with respect to x then we get sinx with negative sign. Thus total term by differentiating we get 2sinxcosx with negative sign.
We have to write the result in more accurate form. For this we have to use trigonometric rules. By using these rules we get 2sinxcosx in another form is sin2x.so we use this form.
Finally derivative of Cos X Squared we get 2sinxcosx or sin2x with negative sign.
d/dx(cosx)^2=(-sin2x)
