What is the derivative of sqrt(4ax) ?

The derivative of sqrt(4ax) is sqrt(a/x)

What is the first derivative of sqrt(4ax) ?

The first derivative of sqrt(4ax) is sqrt(a/x)

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

\frac{a}{x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}

What is the derivative of sqrt(4ax) ?
The derivative of sqrt(4ax) is sqrt(a/x)
What is the first derivative of sqrt(4ax) ?
The first derivative of sqrt(4ax) is sqrt(a/x)