What is (\partial)/(\partial x)((x^2-y^2)^{1/2}) ?

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

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(\partial)/(\partial x)((x^2-y^2)^{1/2})

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

\frac{x}{( x ^{2} - y ^{2} ) ^{\frac{1}{2}}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int - 2 + 30 x - 12 x^{2} d x

x \to 0 lim ((1 + 4 x)^{\frac{3}{x}})

\int (\frac{tan ( u )}{4} - \frac{4}{7} u^{6} - \frac{2}{u}) d u

x \to a lim (\frac{1}{2})

f (x) = (5 x + 4)^{3}

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