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

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

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

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

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derivative of

f (x) = x - x

\frac{1}{2 x} - 1

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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