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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{d}{d t} (e^{t} sin (9 t))

\int_{0}^{\frac{3 π}{2}} cos^{3} (37 x) d x

\int \frac{cos ( x )}{( 1 - sin ( x ) )} d x

8 x^{2} - x^{3}, x^{2} + 11 x, 0, 5

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