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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1}{( 36 - x ^{2} ) ^{\frac{3}{2}}} d x

(4 t^{5} - 6 t)^{8}

\frac{\partial}{\partial x} (sin (π (x - 5 y)))

\frac{d}{d x} (cosh (x) sinh (x))

\frac{d}{d x} ((\frac{( - 2 x - 1 )}{( - 4 x + 2 )})^{5})

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