What is the derivative of f(x)=(-4)/(sqrt(x)) ?

The derivative of f(x)=(-4)/(sqrt(x)) is 2/(x^{3/2)}

What is the first derivative of f(x)=(-4)/(sqrt(x)) ?

The first derivative of f(x)=(-4)/(sqrt(x)) is 2/(x^{3/2)}

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derivative of

f (x) = \frac{- 4}{x}

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

Solution steps

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

Simplify

\frac{- 4}{x} : - \frac{4}{x}

= \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}}}

n = 1 \sum \infty (\frac{2 π}{3})^{n}

\int \frac{1}{x ( x ^{2} + 2 )} d x

\int x cos^{2} (5 x) d x

x \to - 3 + lim (\frac{x ^{3}}{x ^{2} - 9})

y = tan (e^{x})

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