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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

x y^{^{'}} + 2 y = - 4 e^{x}

\frac{d}{d x} (- 8 x)

x \to 0 + lim (0)

x 7 - x^{2}

\int (18 x + 2) d x

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