derivative of 4sqrt(x)+8x^{3/8}

Lösung

\frac{d}{d x} (4 x + 8 x^{\frac{3}{8}})

\frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}

Schritte zur Lösung

\frac{d}{d x} (4 x + 8 x^{\frac{3}{8}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x) + \frac{d}{d x} (8 x^{\frac{3}{8}})

\frac{d}{d x} (4 x) = \frac{2}{x ^{\frac{1}{2}}}

\frac{d}{d x} (8 x^{\frac{3}{8}}) = \frac{3}{x ^{\frac{5}{8}}}

= \frac{2}{x ^{\frac{1}{2}}} + \frac{3}{x ^{\frac{5}{8}}}

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{3}}{36}

x \to 1 + lim (\frac{1}{x ^{3}})

s l o p e in t erce pt (- 5, - 1), (0, 3)

\frac{d y}{d x} = \frac{y + 1}{x ^{3}}

n = 1 \sum \infty \frac{( 3 x ) ^{n}}{n}