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}

\frac{d}{d x} (\frac{2 x ^{2}}{4 - x ^{2}})

\int_{2}^{4} (x - 9) d x

\int \frac{1}{x ^{2} + x ^{3}} d x

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 6 x e^{2 x}

f (x) = \frac{1}{x + \frac{1}{x}}

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))