Question

Find the given derivative by finding the first few derivatives and observing the pattern that occurs. 298 (sin(x)) 0x 98

Answer 1

98 Given d ( sinx) : ? 98 da s'cx) = cos(x) of "CX) = -siny f"CX 2 = COS X of "'"(x) = sin(x) 4' will result in sin(x). so; every multiple of so, this means th the 96 derivative will result in sin(x) 24 4 ginx iie. d (sinx) d x 4 96 d (sinx) = sinx, & dx 996 Taking next derivative. 97 cosx d (sinx) 97 doc 98 = -sinac. (sinx) dx 98 98 d - sinx - . (sinx) 98 dx

Answer 2

SOLUTION :

d/dx (sin (x)) = cos(x)

=> d2/dx2  (sin (x)) = d/dx (cos (x)) = - sin (x)

=> d3/dx3  (sin (x)) = d/dx (- sin (x)) = - cos  (x)

=> d4/dx4  (- sin (x)) = d/dx (- cos (x)) = sin (x)

Every 4th derivative = sin(x)

So,

d96/dx96 (sin (x)) = sin (x)

=> d97/dx97 (sin (x)) = cos (x)

=> d98/dx98 (sin (x)) = - sin (x)  (ANSWER).