What is xcos(x)(1/2 x^2) ?

The solution to xcos(x)(1/2 x^2) is (x^3cos(x))/2

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simplify xcos(x)(1/2 x^2)

simplify

x cos (x) (\frac{1}{2} x^{2})

\frac{x ^{3} cos ( x )}{2}

Solution steps

x cos (x) (\frac{1}{2} x^{2})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x x^{2} = x^{1 + 2}

= cos (x) \frac{1}{2} x^{1 + 2}

Add the numbers:

1 + 2 = 3

= cos (x) \frac{1}{2} x^{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x ^{3}}{2} cos (x)

Multiply:

1 \cdot x^{3} = x^{3}

= \frac{x ^{3}}{2} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ^{3} cos ( x )}{2}

(9 \cdot 1 0^{9}) (\frac{( 0.14 \cdot 1 0 ^{- 6} ) ^{2}}{0.2 5 ^{2}})

(8640 0^{2}) (6.673 \cdot 1 0^{- 11}) (5.974 \cdot 1 0^{24})

(4 x y^{3}) (x^{4} y^{3})

e^{- 3} \frac{3 ^{4}}{4 !}