Question

Find the given derivative by finding the first few derivatives and observing the pattern that occurs.

d^114 /dx^114 of (sinx)

Answer 1

Can you use the equation editor to make it more clear?

Answer 2

\[f(x)=\sin x;~~f'(x)=\cos x;~~f"(x)=-\sin x;~~f^{(3)}(x)= -\cos x;~~f^{(4)}(x)= \sin x\]

Answer 3

With this pattern, every fourth one is the same; that makes the 114th derivative is the same as the second derivative. We know this since 114/4 has a remainder of two.

Answer 4

Thanks guys!