What is the derivative of x+1/(sqrt(x)) ?

The derivative of x+1/(sqrt(x)) is 1-1/(2x^{3/2)}

What is the first derivative of x+1/(sqrt(x)) ?

The first derivative of x+1/(sqrt(x)) is 1-1/(2x^{3/2)}

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

1 - \frac{1}{2 x ^{\frac{3}{2}}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= 1 - \frac{1}{2 x ^{\frac{3}{2}}}

x \to - 1 lim (- x^{2} + 4 x - 8)

\int cos^{5} (3 y) d y

x \to 0 lim (\frac{cos ( x )}{x})

y \to 0 lim (sin (\frac{1}{y}))

\frac{d}{d x} (tan (e^{x}) \cdot cosh (e^{x}))

What is the derivative of x+1/(sqrt(x)) ?
The derivative of x+1/(sqrt(x)) is 1-1/(2x^{3/2)}
What is the first derivative of x+1/(sqrt(x)) ?
The first derivative of x+1/(sqrt(x)) is 1-1/(2x^{3/2)}