What is the d/(dy)(ye^{2xy}+x) ?

The d/(dy)(ye^{2xy}+x) is e^{2yx}+2e^{2yx}yx

What is the first d/(dy)(ye^{2xy}+x) ?

The first d/(dy)(ye^{2xy}+x) is e^{2yx}+2e^{2yx}yx

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

e^{2 y x} + 2 e^{2 y x} y x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d x}{d y} = 0

= e^{2 x y} + 2 x e^{2 x y} y + 0

Simplify

= e^{2 y x} + 2 e^{2 y x} y x

What is the d/(dy)(ye^{2xy}+x) ?
The d/(dy)(ye^{2xy}+x) is e^{2yx}+2e^{2yx}yx
What is the first d/(dy)(ye^{2xy}+x) ?
The first d/(dy)(ye^{2xy}+x) is e^{2yx}+2e^{2yx}yx