derivative of 3/(2sqrt(x))

Lösung

\frac{d}{d x} (\frac{3}{2 x})

- \frac{3}{4 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{2 x})

Entferne die Konstante:

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

= \frac{3}{2} \frac{d}{d x} (\frac{1}{x})

Wende Exponentenregel an:

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

= \frac{3}{2} \frac{d}{d x} (x^{- \frac{1}{2}})

Wende die Potenzregel an:

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

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

Vereinfache

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

= - \frac{3}{4 x ^{\frac{3}{2}}}

t an g e n t f (x) = 2 x + 77, at x = 2

x \to 0 - lim (\frac{( 6 x )}{x ^{4}})

y^{^{''}} - 8 y^{^{'}} + 7 y = 0

\int_{0}^{5} (140 x^{2} + 9800) d x

x \to 7 lim (4)