Question

Find the 30th derivative of y=cos(2x)

Answer 1

I got this answer from someone else so I’m not sure this is correct but I really hope it helps...

Step-by-step explanation:

Look for patterns in the derivatives.

y=cos2x

y'=-2sin2x

y''=-4cos2x

y'''=8sin2x

y''''=16cos2x

Notice that sin and cos alternate every derivative. Also, they alternate positive and negative every 2 derivatives.

The constant is just 2^(derivative#).

Every odd derivative has sin and every even derivative has cos, so you know that the 30th derivative will be cos.

If you follow the pattern of negatives and positives, you find that the 30th derivative will be negative.

y^(30)= -2^30cos2x

y^(30)= -1073741824cos2x