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

The answer to (\partial)/(\partial x)(sqrt(2(x+c))) is 1/(sqrt(2)\sqrt{x+c)}

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(\partial)/(\partial x)(sqrt(2(x+c)))

\frac{\partial}{\partial x} (2 (x + c))

\frac{1}{2 x + c}

Solution steps

\frac{\partial}{\partial x} (2 (x + c))

Apply the chain rule:

\frac{1}{2 2 ( x + c )} \frac{\partial}{\partial x} (2 (x + c))

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

\frac{\partial}{\partial x} (2 (x + c)) = 2

= \frac{1}{2 2 ( x + c )} \cdot 2

Simplify

\frac{1}{2 2 ( x + c )} \cdot 2 : \frac{1}{2 x + c}

= \frac{1}{2 x + c}

What is (\partial)/(\partial x)(sqrt(2(x+c))) ?
The answer to (\partial)/(\partial x)(sqrt(2(x+c))) is 1/(sqrt(2)\sqrt{x+c)}