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

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

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

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

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derivative

1 + \frac{1}{2 x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

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