derivative of (400/(1+1/8 sqrt(x))+200)

Lösung

\frac{d}{d x} (\frac{400}{1 + \frac{1}{8} x} + 200)

- \frac{1600}{x ( x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{400}{1 + \frac{1}{8} x} + 200)

Vereinfache

\frac{400}{1 + \frac{1}{8} x} + 200 : \frac{3200}{8 + x} + 200

= \frac{d}{d x} (\frac{3200}{8 + x} + 200)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{3200}{8 + x}) + \frac{d}{d x} (200)

\frac{d}{d x} (\frac{3200}{8 + x}) = - \frac{1600}{x ( x + 8 ) ^{2}}

\frac{d}{d x} (200) = 0

= - \frac{1600}{x ( x + 8 ) ^{2}} + 0

Vereinfache

= - \frac{1600}{x ( x + 8 ) ^{2}}

d er i v a t i v e \frac{, at}{B t ^{2} + C t ^{3}}

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d er i v a t i v e y = 1.45 e^{59.9 t} sin (201 t)

\int_{2}^{6} t^{4} ln (3 t) d t