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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{x ^{2} + 2 x}{( x + 1 ) ^{2}})

y = a^{4} + cos^{4} (x)

\int [5 sin^{2} (3 x) + tan (2 x)] d x

\frac{d}{d x} (4 x + 8 + \frac{14400}{x})

\int 2 x + 4 e^{x} d x

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