What is expand (xcos(x))(cos(x)-xsin(x)) ?

The solution to expand (xcos(x))(cos(x)-xsin(x)) is xcos^2(x)-x^2cos(x)sin(x)

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expand (xcos(x))(cos(x)-xsin(x))

expand

(x cos (x)) (cos (x) - x sin (x))

x cos^{2} (x) - x^{2} cos (x) sin (x)

Solution steps

(x cos (x)) (cos (x) - x sin (x))

Apply the distributive law:

a (b - c) = ab - a c

(x cos (x)) (cos (x) - x sin (x)) = x cos (x) cos (x) - x cos (x) x sin (x)

= x cos (x) cos (x) - x cos (x) x sin (x)

Simplify

x cos (x) cos (x) - x cos (x) x sin (x) : x cos^{2} (x) - x^{2} cos (x) sin (x)

= x cos^{2} (x) - x^{2} cos (x) sin (x)

\frac{1}{x ^{3}} (\frac{d y}{d x} - \frac{3}{x} y = x^{4})

(x + 2 i)^{4}

10 (x + Δ x)^{2}

(x + 2 i)^{3}

\frac{2 ( x ^{4} - 3 x ^{2} )}{( x ^{2} - 1 ) ^{2}}

What is expand (xcos(x))(cos(x)-xsin(x)) ?
The solution to expand (xcos(x))(cos(x)-xsin(x)) is xcos^2(x)-x^2cos(x)sin(x)