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Popular >

derivative of-4/(sqrt(x))

Solution

\frac{d}{d x} (- \frac{4}{x})

Solution

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

Solution steps

\frac{d}{d x} (- \frac{4}{x})

Take the constant out:

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

= - 4 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= - 4 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= - 4 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

- 4 (- \frac{1}{2} x^{- \frac{1}{2} - 1}) : \frac{2}{x ^{\frac{3}{2}}}

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

Popular Examples

limit as x approaches pi/2 of 2tan(x)

x \to \frac{π}{2} lim (2 tan (x))

integral of (8-128x)/(sqrt(25-64x^2))

\int \frac{8 - 128 x}{25 - 64 x ^{2}} d x

f (x) = x^{- 6}

integral of 1/(x^2+8x+17)

\int \frac{1}{x ^{2} + 8 x + 17} d x

(d^4)/(dx^4)(e^{-x^2})

\frac{d ^{4}}{d x ^{4}} (e^{- x^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of-4/(sqrt(x)) ?
The derivative of-4/(sqrt(x)) is 2/(x^{3/2)}
What is the first derivative of-4/(sqrt(x)) ?
The first derivative of-4/(sqrt(x)) is 2/(x^{3/2)}