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

The answer to (\partial)/(\partial x)(sqrt(x)e^{xy}) is (e^{xy})/(2sqrt(x))+e^{xy}ysqrt(x)

Popular >

(\partial)/(\partial x)(sqrt(x)e^{xy})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x y}

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

\frac{\partial}{\partial x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} e^{x y} + e^{x y} y x

\frac{1}{2 x} e^{x y} = \frac{e ^{x y}}{2 x}

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

y^{^{'}} = \frac{x y ( 4 - y )}{1 + x}

\frac{d}{d x} (x^{4} - 25 x^{2} + 144)

\frac{\partial}{\partial x} (x (x^{2} + y^{2})^{\frac{1}{2}})

y = 9 e^{9 e^{x} + x}

1 + e^{x}

What is (\partial)/(\partial x)(sqrt(x)e^{xy}) ?
The answer to (\partial)/(\partial x)(sqrt(x)e^{xy}) is (e^{xy})/(2sqrt(x))+e^{xy}ysqrt(x)