Question

Determine the 77th derivative of y=sin(3x)

Answer 1

You will definitely want to figure out the pattern here :-)

Answer 2

you can figure out the pattern by finding the first few derivatives

Answer 3

like finding: \[f^{(1)},f^{(2)},f^{(3)},f^{(4)}....\]

Answer 4

\[y=\sin 3x\]
\[y'=3\cos(3x)=3\sin((\pi \div 2)+3x)\]
\[y''=3^2\cos ((\pi \div 2)+3x)=3^2\sin ((2\pi \div 2)+3x)\]
\[y ^{n}=3^n \sin (n( \pi \div2)+3x)\]