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Derivative of sin(x)·x²
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Practice · Algebra
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Find the derivative of f(x) = sin(x) · x²
f ′(x) = 2x·sin(x) + x²·cos(x) ✓
Product Rule
d/dx[u·v] = u′v + uv′, where u = x², v = sin(x)
Step 1, differentiate x²
u′ = 2x
Step 2, differentiate sin(x)
v′ = cos(x)
Step 3, combine
f ′(x) = (2x)·sin(x) + x²·cos(x)
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