What is (\partial)/(\partial x)(sqrt(25+x^2)) ?

The answer to (\partial)/(\partial x)(sqrt(25+x^2)) is x/(sqrt(25+x^2))

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(\partial)/(\partial x)(sqrt(25+x^2))

\frac{\partial}{\partial x} (25 + x^{2})

\frac{x}{25 + x ^{2}}

Solution steps

\frac{\partial}{\partial x} (25 + x^{2})

Apply the chain rule:

\frac{1}{2 25 + x ^{2}} \frac{\partial}{\partial x} (25 + x^{2})

= \frac{1}{2 25 + x ^{2}} \frac{\partial}{\partial x} (25 + x^{2})

\frac{\partial}{\partial x} (25 + x^{2}) = 2 x

= \frac{1}{2 25 + x ^{2}} \cdot 2 x

Simplify

\frac{1}{2 25 + x ^{2}} \cdot 2 x : \frac{x}{25 + x ^{2}}

= \frac{x}{25 + x ^{2}}

What is (\partial)/(\partial x)(sqrt(25+x^2)) ?
The answer to (\partial)/(\partial x)(sqrt(25+x^2)) is x/(sqrt(25+x^2))