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(d)/(dx)[cos(x)x^(2)]=

$\frac{d}{d x}\left[\cos (x) x^{2}\right]=$

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Csc, sec, and cot of special angles

Full solution

Q.

\frac{d}{d x}\left[\cos (x) x^{2}\right]=

Apply Product Rule: Use the product rule for differentiation, which states that $(\frac{d}{dx})[u*v] = u'v + uv'$ , where $u = \cos(x)$ and $v = x^2$ .
Differentiate $u$ : Differentiate $u = \cos(x)$ to get $u' = -\sin(x)$ .
Differentiate $v$ : Differentiate $v = x^2$ to get $v' = 2x$ .
Apply Product Rule Formula: Plug $u'$ , $v$ , $u$ , and $v'$ into the product rule formula: $(-\sin(x))(x^2) + (\cos(x))(2x)$ .
Simplify Expression: Simplify the expression: $-x^2 \sin(x) + 2x \cos(x)$ .

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