What is (\partial)/(\partial x)(x^3y^2-2xe^{xy}) ?

The answer to (\partial)/(\partial x)(x^3y^2-2xe^{xy}) is 3y^2x^2-2(e^{yx}+ye^{yx}x)

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(\partial)/(\partial x)(x^3y^2-2xe^{xy})

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

3 y^{2} x^{2} - 2 (e^{y x} + y e^{y x} x)

Solution steps

\frac{\partial}{\partial x} (x^{3} y^{2} - 2 x e^{x y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} y^{2}) - \frac{\partial}{\partial x} (2 x e^{x y})

\frac{\partial}{\partial x} (x^{3} y^{2}) = 3 y^{2} x^{2}

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

= 3 y^{2} x^{2} - 2 (e^{y x} + y e^{y x} x)

\int cot (y) csc^{2} (y) d y

y^{^{''}} - 4 y^{^{'}} + 3 y = x

y^{^{'}} - \frac{6}{x} y = \frac{y ^{4}}{x ^{3}}

x \to 0 lim (\frac{arcsin ( x )}{7 x})

f (x) = sin^{4} (x), g (x) = sin^{2} (x)

What is (\partial)/(\partial x)(x^3y^2-2xe^{xy}) ?
The answer to (\partial)/(\partial x)(x^3y^2-2xe^{xy}) is 3y^2x^2-2(e^{yx}+ye^{yx}x)