Derivatives using chain rule

1. Jun 12, 2014

TommG

Need to find the Derivative using the chain rule

y = x2sin4(x) + xcos-2(x)

I am not sure where to start.

2xsin4(x) + 4x2sin3(x)cos(x) + cos-2(x) +2xcos-3(x) xsin(x)

2. Jun 12, 2014

TommG

I am not sure if I did it right but I think I got the answer.

x2sin4(x)
2xsin4 took derivative of just x2
4x2sin3x derivative of just power of sin
cosx derivative of just sin

2xsin4(x)+4x2sin3(x)cos(x)

xcos-2(x)

cos-2 derivative of x
-2xcos-3(x) derivative of power of cos
-xsin(x) derivative of just cos

cos-2+2xcos-3(x)sin(x)

2xsin4(x)+4x2sin3(x)cos(x)+cos-2(x)+2xcos-3(x)xsin(x)

Last edited: Jun 12, 2014
3. Jun 12, 2014

1MileCrash

Yes, but your work is very strange and hard to read, and I think it makes it more difficult than it should be.

Also, tidy up your penmanship a bit. sin² doesn't mean anything.

Just some suggestions.