What is (\partial)/(\partial x)(sqrt(x^2+y^2+1)) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+y^2+1)) is x/(sqrt(x^2+y^2+1))

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(\partial)/(\partial x)(sqrt(x^2+y^2+1))

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

\frac{x}{x ^{2} + y ^{2} + 1}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

y = 4 ln (cos (x))

\int \frac{x ^{2} - 4}{x ^{4}} d x

\frac{x}{x + 6}

\int (2 x^{2} - 3)^{5} x d x

y = 24 (x^{3} + 6 x)^{\frac{3}{8}}

What is (\partial)/(\partial x)(sqrt(x^2+y^2+1)) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+y^2+1)) is x/(sqrt(x^2+y^2+1))