What is (\partial)/(\partial x)(sqrt(4ax)) ?

The answer to (\partial)/(\partial x)(sqrt(4ax)) is sqrt(a/x)

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(\partial)/(\partial x)(sqrt(4ax))

\frac{\partial}{\partial x} (4 a x)

\frac{a}{x}

Solution steps

\frac{\partial}{\partial x} (4 a x)

Apply the chain rule:

\frac{1}{2 4 a x} \frac{\partial}{\partial x} (4 a x)

= \frac{1}{2 4 a x} \frac{\partial}{\partial x} (4 a x)

\frac{\partial}{\partial x} (4 a x) = 4 a

= \frac{1}{2 4 a x} \cdot 4 a

Simplify

\frac{1}{2 4 a x} \cdot 4 a : \frac{a}{x}

= \frac{a}{x}

\frac{d}{d x} ((x^{2} + 6)^{9})

\frac{d}{d x} (cosh (4 x))

\int \frac{2 x ^{2} + 7 x - 8}{x - 7} d x

\frac{\partial}{\partial y} (e^{2 x + 3 y})

x \to 1 + lim (x + 2)

What is (\partial)/(\partial x)(sqrt(4ax)) ?
The answer to (\partial)/(\partial x)(sqrt(4ax)) is sqrt(a/x)