What is expand cos(x^2+3y-1)(2x+3(dy)/(dx)) ?

The solution to expand cos(x^2+3y-1)(2x+3(dy)/(dx)) is 2xcos(x^2+3y-1)+3cos(x^2+3y-1)(dy)/(dx)

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expand cos(x^2+3y-1)(2x+3(dy)/(dx))

expand

cos (x^{2} + 3 y - 1) (2 x + 3 \frac{d y}{d x})

2 x cos (x^{2} + 3 y - 1) + 3 cos (x^{2} + 3 y - 1) \frac{d y}{d x}

Solution steps

cos (x^{2} + 3 y - 1) (2 x + 3 \frac{d y}{d x})

Apply the distributive law:

a (b + c) = ab + a c

a = cos (x^{2} + 3 y - 1), b = 2 x, c = 3 \frac{d y}{d x}

= cos (x^{2} + 3 y - 1) \cdot 2 x + cos (x^{2} + 3 y - 1) \cdot 3 \frac{d y}{d x}

= 2 x cos (x^{2} + 3 y - 1) + 3 cos (x^{2} + 3 y - 1) \frac{d y}{d x}

\frac{5 x ^{3} + 14 x ^{2} + 23 x + 6}{( s + 3 ) \cdot ( s - 3 ) \cdot ( s + 1 ) ^{2}}

1 + \frac{1}{s ( s + 2.2 )}

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

\frac{1}{( s + 2 ) ( s + 3 )}

\frac{d}{d z} ((w) (3 z^{7} - 7 z^{3} + 21 z^{2}))

What is expand cos(x^2+3y-1)(2x+3(dy)/(dx)) ?
The solution to expand cos(x^2+3y-1)(2x+3(dy)/(dx)) is 2xcos(x^2+3y-1)+3cos(x^2+3y-1)(dy)/(dx)