What is (\partial)/(\partial x)(sqrt(x-y^2)) ?

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

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(\partial)/(\partial x)(sqrt(x-y^2))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

x \to 0 lim (3^{x})

\int x^{3} 7 + x^{4} d x

x^{6}, x^{7}

\int_{0}^{\frac{π}{4}} tan^{4} (x) d x

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

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