Question

find d^2y/dx^2

y = x^2 (sinx + cosx)

Answer 1

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Hope this answer will help u....

Answer 2

Answer:

d²y/dx² = ( 2 - x²)(Sinx + cosx) - -4x(Sinx - Cosx)

Step-by-step explanation:

y = x²(sinx + cosx)

=> y = x²Sinx  + x²Cosx

dy/dx = x²Cosx + 2xSinx  + x²(-Sinx) + 2xCosx

d²y/dx² = x²(-sinx) + 2xCosx + 2xCosx + 2Sinx - x²Cosx - 2xSinx +2x(-sinx) + 2Cosx

= -x²Sinx - x²Cosx + 4xCosx -4xSinx + 2Sinx + 2Cosx

= -x²(Sinx + cosx)  -4x(Sinx - Cosx) + 2(Sinx + Cosx)

= ( 2 - x²)(Sinx + cosx)  -4x(Sinx - Cosx)

d²y/dx² = ( 2 - x²)(Sinx + cosx)  -4x(Sinx - Cosx)