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Beliebt Rechnen >

derivative 2^{x+3}

Lösung

ableitung von

2^{x + 3}

Lösung

ln (2) \cdot 2^{x + 3}

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

2^{x + 3} = e^{(x + 3) l n (2)}

= \frac{d}{d x} (e^{(x + 3) l n (2)})

Wende die Kettenregel an:

e^{(x + 3) l n (2)} \frac{d}{d x} ((x + 3) ln (2))

= e^{(x + 3) l n (2)} \frac{d}{d x} ((x + 3) ln (2))

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

= e^{(x + 3) l n (2)} ln (2)

e^{(x + 3) l n (2)} = 2^{x + 3}

= ln (2) \cdot 2^{x + 3}

Graph

Beliebte Beispiele

integral of (x^3)/(\sqrt[3]{x^2+3)}

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

laplacetransform Y^3

l a pl a ce t r an s f or m Y^{3}

integral of y/4

\int \frac{y}{4} d y

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

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

y^{''}-4y^'+7y=xe^x

y^{^{''}} - 4 y^{^{'}} + 7 y = x e^{x}