derivative of (x-sqrt(x)/(x^{1/9)})

Lösung

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{9}}})

\frac{7 ( x - 1 )}{18 x ^{\frac{11}{18}}} + \frac{1}{2 x ^{\frac{1}{9}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{9}}})

Vereinfache

\frac{x - x}{x ^{\frac{1}{9}}} : x^{\frac{7}{18}} (x - 1)

= \frac{d}{d x} (x^{\frac{7}{18}} (x - 1))

Wende die Produktregel an:

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

f = x^{\frac{7}{18}}, g = x - 1

= \frac{d}{d x} (x^{\frac{7}{18}}) (x - 1) + \frac{d}{d x} (x - 1) x^{\frac{7}{18}}

\frac{d}{d x} (x^{\frac{7}{18}}) = \frac{7}{18 x ^{\frac{11}{18}}}

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

= \frac{7}{18 x ^{\frac{11}{18}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{7}{18}}

Vereinfache

\frac{7}{18 x ^{\frac{11}{18}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{7}{18}} : \frac{7 ( x - 1 )}{18 x ^{\frac{11}{18}}} + \frac{1}{2 x ^{\frac{1}{9}}}

= \frac{7 ( x - 1 )}{18 x ^{\frac{11}{18}}} + \frac{1}{2 x ^{\frac{1}{9}}}

a re a y = 2 x + 5, y = 14 - x^{2}, (- 1, 2)

\frac{d}{d x} (- 3 sin (x) + cos (x))

\int \frac{8 x ^{3} + 13 x}{( x ^{2} + 2 ) ^{2}} d x

\int_{1}^{3} (3 x^{2} - 2 x + 1) d x

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