What is the derivative of f(x)=3(sqrt(x+1)) ?

The derivative of f(x)=3(sqrt(x+1)) is 3/(2sqrt(x+1))

What is the first derivative of f(x)=3(sqrt(x+1)) ?

The first derivative of f(x)=3(sqrt(x+1)) is 3/(2sqrt(x+1))

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derivative of

f (x) = 3 (x + 1)

\frac{3}{2 x + 1}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of f(x)=3(sqrt(x+1)) ?
The derivative of f(x)=3(sqrt(x+1)) is 3/(2sqrt(x+1))
What is the first derivative of f(x)=3(sqrt(x+1)) ?
The first derivative of f(x)=3(sqrt(x+1)) is 3/(2sqrt(x+1))