What is the derivative of f(x)=16sqrt(x+3) ?

The derivative of f(x)=16sqrt(x+3) is 8/(sqrt(x+3))

What is the first derivative of f(x)=16sqrt(x+3) ?

The first derivative of f(x)=16sqrt(x+3) is 8/(sqrt(x+3))

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derivative of

f (x) = 16 x + 3

\frac{8}{x + 3}

Solution steps

\frac{d}{d x} (16 x + 3)

Take the constant out:

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

= 16 \frac{d}{d x} (x + 3)

Apply the chain rule:

\frac{1}{2 x + 3} \frac{d}{d x} (x + 3)

= \frac{1}{2 x + 3} \frac{d}{d x} (x + 3)

\frac{d}{d x} (x + 3) = 1

= 16 \cdot \frac{1}{2 x + 3} \cdot 1

Simplify

16 \cdot \frac{1}{2 x + 3} \cdot 1 : \frac{8}{x + 3}

= \frac{8}{x + 3}

What is the derivative of f(x)=16sqrt(x+3) ?
The derivative of f(x)=16sqrt(x+3) is 8/(sqrt(x+3))
What is the first derivative of f(x)=16sqrt(x+3) ?
The first derivative of f(x)=16sqrt(x+3) is 8/(sqrt(x+3))