Question

Is the following true or false?

The 12th derivative of sin(x) = cos(x).

Answer 1

you're going to need to try to get the derivative of \(sin (x) \) then derive \(cos (x) \) until you reach the 12th derivative doing the same thing over and over

Answer 2

Its false because it would be equal to -cos correct?

Answer 3

the derivatives of sin have a pattern

Answer 4

The pattern is , starting with sin,
sin , cos, -sin, -cos, sin , ...

Answer 5

\[\sin^{(n)}(x) = \sin \left(\frac{n\pi}{2}+x\right)\]

Answer 6

Does it follow the pattern he says it does because if it does then it is true

Answer 7

Yes, yes it does.

Answer 8

Okay thank you!