derivative of \sqrt[7]{x}+2sqrt(x^7)

Lösung

\frac{d}{d x} (7 x + 2 x^{7})

\frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d x} (7 x + 2 x^{7})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x) + \frac{d}{d x} (2 x^{7})

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

\frac{d}{d x} (2 x^{7}) = 7 x^{\frac{5}{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} + 7 x^{\frac{5}{2}}

Vereinfache

\frac{1}{7 x ^{\frac{6}{7}}} + 7 x^{\frac{5}{2}} : \frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

= \frac{1 + 49 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

\int x^{7} e^{- x^{4}} d x

\int lo g_{b} (x) d x

a re a y + x = 4, 36 - 9 x = y^{2}

\frac{d}{d t} (A \cdot (cos (ω t + φ)))

y^{^{'}} (x) = \frac{x ^{2}}{1 - y ^{2}}, y (4) = 2