What is the derivative of f(x)=x^{-1/2} ?

The derivative of f(x)=x^{-1/2} is -1/(2x^{3/2)}

What is the first derivative of f(x)=x^{-1/2} ?

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

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derivative of

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

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

Solution steps

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

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

y^{^{''}} - 3 y^{^{'}} + 4 y = 2, y (0) = 0, y^{^{'}} (0) = 0

\frac{d s}{d t}

\int_{1}^{2} 2 e^{- 2 x} d x

\frac{\partial}{\partial x} (2 x - 4 y)

h (x) = 5 sin^{3} (3 + x)

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