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

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

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

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

\frac{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}) = 2 x

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

Simplify

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

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

\int 21 tan^{3} (x) d x

\frac{d}{d x} (6 (x)^{3} - 3 (x) (y) + 3 (y)^{3})

\int_{0}^{5} \frac{6}{7 x ^{2} + 8 x + 1} d x

\int x^{2} (4 x^{3} + 2)^{3} d x

y = x^{2}, (- 1, - 3)

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