What is expand (4ye^{4xy}-3/y)dx ?

The solution to expand (4ye^{4xy}-3/y)dx is 4e^{4yx}ydx-(3dx)/y

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expand (4ye^{4xy}-3/y)dx

expand

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

4 e^{4 y x} y d x - \frac{3 d x}{y}

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = d x, b = 4 y e^{4 x y}, c = \frac{3}{y}

= d x \cdot 4 y e^{4 x y} - d x \frac{3}{y}

= 4 e^{4 y x} y d x - \frac{3}{y} d x

Multiply

\frac{3}{y} d x : \frac{3 d x}{y}

= 4 e^{4 y x} y d x - \frac{3 d x}{y}

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(7 x^{2} + 1) \cdot \frac{d ^{2} y}{d x ^{2}}

What is expand (4ye^{4xy}-3/y)dx ?
The solution to expand (4ye^{4xy}-3/y)dx is 4e^{4yx}ydx-(3dx)/y