What is the derivative of sqrt(16x+1) ?

The derivative of sqrt(16x+1) is 8/(sqrt(16x+1))

What is the first derivative of sqrt(16x+1) ?

The first derivative of sqrt(16x+1) is 8/(sqrt(16x+1))

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\frac{d}{d x} (16 x + 1)

\frac{8}{16 x + 1}

Solution steps

\frac{d}{d x} (16 x + 1)

Apply the chain rule:

\frac{1}{2 16 x + 1} \frac{d}{d x} (16 x + 1)

= \frac{1}{2 16 x + 1} \frac{d}{d x} (16 x + 1)

\frac{d}{d x} (16 x + 1) = 16

= \frac{1}{2 16 x + 1} \cdot 16

Simplify

\frac{1}{2 16 x + 1} \cdot 16 : \frac{8}{16 x + 1}

= \frac{8}{16 x + 1}

What is the derivative of sqrt(16x+1) ?
The derivative of sqrt(16x+1) is 8/(sqrt(16x+1))
What is the first derivative of sqrt(16x+1) ?
The first derivative of sqrt(16x+1) is 8/(sqrt(16x+1))