What is the derivative of cos x?

Answer 1

I believe it's sin x, with a negative in front.

Answer 2

It is -sin x.
You can get this either from the definition of derivative
or by using the fact that the derivative of sin x is cos x,
writing
y = √(1-sin² x) and using the chain rule.

Answer 3

The derivative with respect to x of cos x is - sin x. The derivative with respect to anything else, let's call it u, is (-sin x) dx/du.

Answer 4

using the first principle of derivative, let f(x) = cosx
now by principle: f(x + h) = cos(x + h)

f(x+h) - f(x) all over h --------- 1

i.e cos(x + h) - cos(x) / h
but cos(x + h) = cosxcoxh - sinxsinh

now substutiing into ----1

we have : cosxcosh - sinxsinh - cosx / h
bringing the common term cosx out

cosx(cosh - 1 - sinxsinh) / h
cosx(cosh - 1) / h - sinxsinh / h
but sinh/h = 1

so then: cosx(cosh - 1) / h - sinx(1)

take h = 0

cosx (cos*(0) - 1) / 0 - sinx

therefore derivative of cosx = -sinx

Answer 5

If x is measured in radians (the default), then the derivative is -sin(x). If x is measured in degrees, the derivative is (-pi/180)sin(x).

Answer 6

the answer is -sinx
you can find this result using limit

lim [ (cos(x+h)-cos(x)] /h
h-->0

as you see this is 0/0
that is indefinite
use cos p - cos q expansion

Answer 7

-sin x.

Answer 8

-sinx

Answer 9

-sinx

Answer 10

- sin (x)