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

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

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

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

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derivative of

\frac{1}{( x )}

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

Solution steps

\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}}}

\frac{d}{d x} (2 cos (10 x) + 2 sin (4 y) + 10 x - 4 y)

1 + ∣ x ∣

\frac{d}{d x} (3 e^{x} - 0.4 y)

\frac{x ^{1}}{x}

\frac{lo g _{10} ( x )}{x ^{2}}

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