What is the derivative of sqrt(ax+b) ?

The derivative of sqrt(ax+b) is a/(2sqrt(ax+b))

What is the first derivative of sqrt(ax+b) ?

The first derivative of sqrt(ax+b) is a/(2sqrt(ax+b))

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\frac{d}{d x} (a x + b)

\frac{a}{2 a x + b}

Solution steps

\frac{d}{d x} (a x + b)

Apply the chain rule:

\frac{1}{2 a x + b} \frac{d}{d x} (a x + b)

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

\frac{d}{d x} (a x + b) = a

= \frac{1}{2 a x + b} a

Simplify

\frac{1}{2 a x + b} a : \frac{a}{2 a x + b}

= \frac{a}{2 a x + b}

What is the derivative of sqrt(ax+b) ?
The derivative of sqrt(ax+b) is a/(2sqrt(ax+b))
What is the first derivative of sqrt(ax+b) ?
The first derivative of sqrt(ax+b) is a/(2sqrt(ax+b))