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QUESTION:
y = x² sinx , find
ANSWER:
d²y / dx² = 2 sin x + 4x cos x - x² sin x
GIVEN:
y = x² sinx
TO FIND:
d²y / dx²
FORMULAE:
dx/dx = 1
d/dx(uv) = uv' + vu'
d/dx (x²) = 2x
d/dx(sin x) = cos x
EXPLANATION:
dy /dx = d/dx (x²) sin x + d/dx(sin x) (x²)
dy /dx = 2x(sin x) dx/dx + x² (cos x ) dx/dx
dy /dx = 2x sin x + x² cos x
d²y / dx² = 2(dx/dx sin x + x d/dx(sin x)) + d/dx(x²) cos x + x² d/dx(cos x))
d²y / dx² = 2( sin x + x cos x) + 2x cos x + x²(- sin x)
d²y / dx² = 2 sin x + 2x cos x + 2x cos x - x² sin x
d²y / dx² = 2 sin x + 4x cos x - x² sin x
Hence = 2 sin x + 4x cos x - x² sin x
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