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

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

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

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

y^{2} - e^{x y} y

Solution steps

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

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

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

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

y^{^{''}} + 20 y^{^{'}} + 200 y = 300, y (0) = 0, y^{^{'}} (0) = 0

f (x) = 9 + 8 x + 6 x e^{x}, at x = 0

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

t \to 1 lim (\frac{2 t}{t ^{2} - 1})

n = 1 \sum \infty 3 (5)^{- n}

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