What is the derivative of f(x)=sqrt(x+9) ?

The derivative of f(x)=sqrt(x+9) is 1/(2sqrt(x+9))

What is the first derivative of f(x)=sqrt(x+9) ?

The first derivative of f(x)=sqrt(x+9) is 1/(2sqrt(x+9))

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derivative

\frac{1}{2 x + 9}

Solution steps

\frac{d}{d x} (x + 9)

Apply the chain rule:

\frac{1}{2 x + 9} \frac{d}{d x} (x + 9)

= \frac{1}{2 x + 9} \frac{d}{d x} (x + 9)

\frac{d}{d x} (x + 9) = 1

= \frac{1}{2 x + 9} \cdot 1

Simplify

= \frac{1}{2 x + 9}

What is the derivative of f(x)=sqrt(x+9) ?
The derivative of f(x)=sqrt(x+9) is 1/(2sqrt(x+9))
What is the first derivative of f(x)=sqrt(x+9) ?
The first derivative of f(x)=sqrt(x+9) is 1/(2sqrt(x+9))