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Beliebt Rechnen >

derivative of e^{2(x-1^2}+x/(1+x^3))

Lösung

\frac{d}{d x} (e^{2 (x - 1)^{2}} + \frac{x}{1 + x ^{3}})

Lösung

e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{2 (x - 1)^{2}} + \frac{x}{1 + x ^{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (e^{2 (x - 1)^{2}}) + \frac{d}{d x} (\frac{x}{1 + x ^{3}})

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

\frac{d}{d x} (\frac{x}{1 + x ^{3}}) = \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

= e^{2 (x - 1)^{2}} \cdot 4 (x - 1) + \frac{1 - 2 x ^{3}}{( 1 + x ^{3} ) ^{2}}

Graph

Beliebte Beispiele

tangent y=8x+12-15e^x,(0,-3)

t an g e n t y = 8 x + 12 - 15 e^{x}, (0, - 3)

integral of (3+x)/(1+x^2)

\int \frac{3 + x}{1 + x ^{2}} d x

fläche x^2+10,9x,0

a re a x^{2} + 10, 9 x, 0

integral of ((9-y^2)^2)/2-y(9-y^2)

\int \frac{( 9 - y ^{2} ) ^{2}}{2} - y (9 - y^{2}) d y

integral of sqrt(y+4)

\int y + 4 d y