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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} + 5 y = x

\frac{d}{d x} (x^{3} - 3 x^{2} + 3)

\frac{d}{d x} (e^{x} - x^{3} - 7)

\frac{d}{d x} (60 x^{2})

\int e^{c o s (x)} d x

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