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

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

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

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

- e^{y x} y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

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

= 0 - e^{x y} y

Simplify

= - e^{y x} y

\frac{s}{s ^{4} + 1}

\int tan (2 t) d t

y^{^{''}} + 16 y = t e^{4 t}

\frac{y}{x}

(\frac{100}{lo g _{10} ( 2 x + 1 )})^{^{'}}

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