find d^2y/dx^2
y = x^2 (sinx + cosx)
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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)
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