What is expand ycos(xy)(y+x((dy)/(dx))) ?

The solution to expand ycos(xy)(y+x((dy)/(dx))) is cos(xy)y^2+xcos(xy)y(dy)/(dx)

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expand ycos(xy)(y+x((dy)/(dx)))

expand

y cos (x y) (y + x (\frac{d y}{d x}))

cos (x y) y^{2} + x cos (x y) y \frac{d y}{d x}

Solution steps

y cos (x y) (y + x (\frac{d y}{d x}))

= cos (x y) y (y + x (\frac{d y}{d x}))

Apply the distributive law:

a (b + c) = ab + a c

a = y cos (x y), b = y, c = x (\frac{d y}{d x})

= y cos (x y) y + y cos (x y) x (\frac{d y}{d x})

= cos (x y) yy + x cos (x y) y (\frac{d y}{d x})

Simplify

cos (x y) yy + x cos (x y) y (\frac{d y}{d x}) : cos (x y) y^{2} + x cos (x y) y \frac{d y}{d x}

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

5 (3 - 6)

\frac{( x + 3 ) ^{2}}{( x + 5 ) ( x - 3 )}

\frac{cos ( x ) + i sin ( x )}{( cos ( a ) - sin ( a ) i ) ^{2}}

x (x^{4} e^{4 x} + 2)

(s + 3)^{2}

What is expand ycos(xy)(y+x((dy)/(dx))) ?
The solution to expand ycos(xy)(y+x((dy)/(dx))) is cos(xy)y^2+xcos(xy)y(dy)/(dx)