What is the derivative of sqrt(1+4x) ?

The derivative of sqrt(1+4x) is 2/(sqrt(1+4x))

What is the first derivative of sqrt(1+4x) ?

The first derivative of sqrt(1+4x) is 2/(sqrt(1+4x))

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derivative of

1 + 4 x

\frac{2}{1 + 4 x}

Solution steps

\frac{d}{d x} (1 + 4 x)

Apply the chain rule:

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

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

\frac{d}{d x} (1 + 4 x) = 4

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

Simplify

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

= \frac{2}{1 + 4 x}

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What is the derivative of sqrt(1+4x) ?
The derivative of sqrt(1+4x) is 2/(sqrt(1+4x))
What is the first derivative of sqrt(1+4x) ?
The first derivative of sqrt(1+4x) is 2/(sqrt(1+4x))