derivative (sqrt(x)-x)/(x^{1/4)}

Lösung

ableitung von

\frac{x - x}{x ^{\frac{1}{4}}}

\frac{- x + 1}{4 x ^{\frac{3}{4}}} - \frac{1}{2 x ^{\frac{1}{4}}}

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{1}{4}}, g = - x + 1

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

\frac{d}{d x} (x^{\frac{1}{4}}) = \frac{1}{4 x ^{\frac{3}{4}}}

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

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

Vereinfache

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

= \frac{- x + 1}{4 x ^{\frac{3}{4}}} - \frac{1}{2 x ^{\frac{1}{4}}}

t a y l or (1 - x)^{\frac{1}{4}}, 0

\int cos (x + \frac{π}{3}) d x

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