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Beliebt Rechnen >

derivative f(x)=e^{sqrt(x^3+1)}

Lösung

ableitung von

f (x) = e^{x^{3} + 1}

Lösung

\frac{3 e ^{x^{3} + 1} x ^{2}}{2 x ^{3} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= e^{x^{3} + 1} \frac{3 x ^{2}}{2 x ^{3} + 1}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{x^{3} + 1} x ^{2}}{2 x ^{3} + 1}

Graph

Beliebte Beispiele

derivative f(x)=\sqrt[3]{x^5}

d er i v a t i v e f (x) = 3 x^{5}

derivative y= 1/(sqrt(2x-1))

d er i v a t i v e y = \frac{1}{2 x - 1}

derivative f(x)=(x^3+5)/(x^2+1)

d er i v a t i v e f (x) = \frac{x ^{3} + 5}{x ^{2} + 1}

derivative of arccos(2x^2)

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

integral of sqrt(2+t^2)

\int 2 + t^{2} d t