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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - \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}}}

(x + 3)^{\frac{1}{2}}

\int cos (\frac{z}{y}) d z

f (x) = - 3 x^{2} - 2 x^{2} - 1, at x = - 1

\int \frac{cos ( x )}{5 + sin ( x )} d x

11 t^{2} + 9

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