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Beliebt Rechnen >

derivative of sqrt((x+2^2*(x^2)/2))

Lösung

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

Lösung

2 (x + 1)

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 ( x + 2 ) ^{2} \frac{x ^{2}}{2}} \frac{d}{d x} ((x + 2)^{2} \frac{x ^{2}}{2})

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

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

= \frac{1}{2 ( x + 2 ) ^{2} \frac{x ^{2}}{2}} \cdot 2 x (x + 2) (x + 1)

Vereinfache

\frac{1}{2 ( x + 2 ) ^{2} \frac{x ^{2}}{2}} \cdot 2 x (x + 2) (x + 1) : 2 (x + 1)

= 2 (x + 1)

Graph

Beliebte Beispiele

derivative of (e^x/(5x^3))

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{3}})

tangent f(x)=(1+5x)^{12},(0,1)

t an g e n t f (x) = (1 + 5 x)^{12}, (0, 1)

10y^'=10*9.81-5y

10 y^{^{'}} = 10 \cdot 9.81 - 5 y

tangent y= 1/(x-1),\at x=6

t an g e n t y = \frac{1}{x - 1}, at x = 6

y^{''}-4y^'+3y=0

y^{^{''}} - 4 y^{^{'}} + 3 y = 0