What is (\partial)/(\partial x)(sqrt(x^2+y^3)) ?

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

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(\partial)/(\partial x)(sqrt(x^2+y^3))

\frac{\partial}{\partial x} (x^{2} + y^{3})

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

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{3})

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x}{x ^{2} + y ^{3}}

\frac{d}{d x} (\frac{1 - 2 ln ( x )}{4 x ^{3}})

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

\frac{500}{5 t ^{2} + 10 t + 100}

\int \frac{\frac{1}{x}}{ln ( x ) ln ^{2} ( x ) - 1} d x

\frac{d y}{d x} - 7 y = e^{x}

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