What is (\partial)/(\partial x)(sqrt(x^3y-y^4)) ?

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

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(\partial)/(\partial x)(sqrt(x^3y-y^4))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{3} y - y ^{4}} \frac{\partial}{\partial x} (x^{3} y - y^{4})

= \frac{1}{2 x ^{3} y - y ^{4}} \frac{\partial}{\partial x} (x^{3} y - y^{4})

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

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

Simplify

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

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

\int tan^{3} (x) sec^{8} (x) d x

\frac{2}{3} x^{3}

x \to 0 + lim (tan (\frac{2}{x}))

\int e^{x^{2} + 4 x + 3} (x + 2) d x

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

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