derivative (x-sqrt(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}}}

d er i v a t i v e \frac{5}{2} x^{\frac{5}{2}}

t an g e n t f (x) = 2 x^{4} - 10 x^{2}, at x = - 2

\frac{d}{d x} (ln (x - \frac{π}{2}))

x \to \infty lim (42 + x)

y^{^{'}} + y = x + 5