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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = e^{- 5 x^{4}}

y = 4 x + 2, 0, 4

x \to 5 lim (- x^{3})

\frac{1}{s + 1}

n = 1 \sum \infty \frac{n !}{n 5 ^{n}}

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