What is the derivative of asqrt(x+4) ?

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

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

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

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

\frac{a}{2 x + 4}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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