What is (\partial)/(\partial x)(sqrt(4x^2+y^2)) ?

The answer to (\partial)/(\partial x)(sqrt(4x^2+y^2)) is (4x)/(sqrt(4x^2+y^2))

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(\partial)/(\partial x)(sqrt(4x^2+y^2))

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

\frac{4 x}{4 x ^{2} + y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 4 x ^{2} + y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + y^{2})

= \frac{1}{2 4 x ^{2} + y ^{2}} \frac{\partial}{\partial x} (4 x^{2} + y^{2})

\frac{\partial}{\partial x} (4 x^{2} + y^{2}) = 8 x

= \frac{1}{2 4 x ^{2} + y ^{2}} \cdot 8 x

Simplify

\frac{1}{2 4 x ^{2} + y ^{2}} \cdot 8 x : \frac{4 x}{4 x ^{2} + y ^{2}}

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

\int \frac{2 - u}{u ^{2} + 2 u + 3} d u

x \to 4 - lim (2 x - 5)

f (1) = x^{6} + 4 e^{x}

\frac{d}{d x} (4 3 x^{5})

\frac{d}{d x} (sin^{2} (cos (2 x)))

What is (\partial)/(\partial x)(sqrt(4x^2+y^2)) ?
The answer to (\partial)/(\partial x)(sqrt(4x^2+y^2)) is (4x)/(sqrt(4x^2+y^2))