What is (\partial)/(\partial x)(((yx)/(zw))^{1/2}) ?

The answer to (\partial)/(\partial x)(((yx)/(zw))^{1/2}) is (y^{1/2}(zw)^{1/2})/(2zwx^{1/2)}

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(\partial)/(\partial x)(((yx)/(zw))^{1/2})

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

\frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

Solution steps

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

Treat

y, z, w

as constants

Apply the chain rule:

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

= \frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \frac{\partial}{\partial x} (\frac{y x}{z w})

\frac{\partial}{\partial x} (\frac{y x}{z w}) = \frac{y}{z w}

= \frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w}

Simplify

\frac{1}{2 ( \frac{y x}{z w} ) ^{\frac{1}{2}}} \cdot \frac{y}{z w} : \frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

= \frac{y ^{\frac{1}{2}} ( z w ) ^{\frac{1}{2}}}{2 z w x ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{4 - x e ^{x}}{x + e ^{x}})

n = 1 \sum \infty \frac{cos ( nπ )}{n ^{2}}

x \to 2 lim (\frac{x + 47 - 7}{5 x - 10})

\frac{\partial}{\partial x} (y^{5} sin (6 x))

\int_{0}^{1} \int_{0}^{s^{5}} cos (s^{6}) d t d s

What is (\partial)/(\partial x)(((yx)/(zw))^{1/2}) ?
The answer to (\partial)/(\partial x)(((yx)/(zw))^{1/2}) is (y^{1/2}(zw)^{1/2})/(2zwx^{1/2)}