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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

tan (2 (x + 1))

x \to 1 + lim (\frac{x + 2}{1 - x})

\int_{0}^{10} 100 e^{0.1 x} d x

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

\int π ((20 x)^{2} - (5 x)^{2}) d x

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