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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

(y^{3} - 8) 1 + y^{4}

\frac{( s - 2 )}{( s + 4 ) ( s ^{2} + 9 )}

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

\frac{( x ^{2} - 1 ) ^{3}}{( 4 x ^{3} - 5 ) ^{2}}

sin (x) (sin (x) \cdot cos (x) - 2)

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