derivative of 2x^3+1/(x^2+16x^{7/2}+5)

Lösung

\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

\frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5)

Vereinfache

2 x^{3} + \frac{1}{x ^{2}} + 16 x^{\frac{7}{2}} + 5 : \frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}} + 5

= \frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}} + 5)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}}) + \frac{d}{d x} (5)

\frac{d}{d x} (\frac{1 + 2 x ^{5} + 16 x ^{\frac{11}{2}}}{x ^{2}}) = \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

\frac{d}{d x} (5) = 0

= \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}} + 0

Vereinfache

= \frac{2 ( 3 x ^{5} + 28 x ^{\frac{11}{2}} - 1 )}{x ^{3}}

2 x y^{^{'}} + y = 6 x, y (4) = 20

x^{^{''''}} = 0

x \to 5 lim (x)

y^{^{''}} - y^{^{'}} - 6 y = 0, y^{^{'}} (0) = - 6

\int \frac{2 - x}{x ^{2} - x + 1} d x