Derivative of x^2sin(4x) + xcos^(-2x)

[TommG]

Need to find the Derivative using the chain rule

y = x²sin⁴(x) + xcos^-2(x)

I am not sure where to start.

answer in book is
2xsin⁴(x) + 4x²sin³(x)cos(x) + cos^-2(x) +2xcos^-3(x) xsin(x)

 

[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)

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

 

[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.