What is (\partial)/(\partial x)(sqrt(x^4-y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(x^4-y^2)) is (2x^3)/(sqrt(x^4-y^2))

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(\partial)/(\partial x)(sqrt(x^4-y^2))

\frac{\partial}{\partial x} (x^{4} - y^{2})

\frac{2 x ^{3}}{x ^{4} - y ^{2}}

Solution steps

\frac{\partial}{\partial x} (x^{4} - y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{4} - y ^{2}} \frac{\partial}{\partial x} (x^{4} - y^{2})

= \frac{1}{2 x ^{4} - y ^{2}} \frac{\partial}{\partial x} (x^{4} - y^{2})

\frac{\partial}{\partial x} (x^{4} - y^{2}) = 4 x^{3}

= \frac{1}{2 x ^{4} - y ^{2}} \cdot 4 x^{3}

Simplify

\frac{1}{2 x ^{4} - y ^{2}} \cdot 4 x^{3} : \frac{2 x ^{3}}{x ^{4} - y ^{2}}

= \frac{2 x ^{3}}{x ^{4} - y ^{2}}

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 3})

f (x) = cos^{3} (x)

ln (\frac{1}{x})

\int e^{3 x + 2} d x

ln^{2} (x^{2})

What is (\partial)/(\partial x)(sqrt(x^4-y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(x^4-y^2)) is (2x^3)/(sqrt(x^4-y^2))