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Beliebt Rechnen >

derivative y=7^{5x+4}

Lösung

ableitung von

y = 7^{5 x + 4}

Lösung

5 ln (7) \cdot 7^{5 x + 4}

Schritte zur Lösung

\frac{d}{d x} (7^{5 x + 4})

Wende Exponentenregel an:

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

7^{5 x + 4} = e^{(5 x + 4) l n (7)}

= \frac{d}{d x} (e^{(5 x + 4) l n (7)})

Wende die Kettenregel an:

e^{(5 x + 4) l n (7)} \frac{d}{d x} ((5 x + 4) ln (7))

= e^{(5 x + 4) l n (7)} \frac{d}{d x} ((5 x + 4) ln (7))

\frac{d}{d x} ((5 x + 4) ln (7)) = 5 ln (7)

= e^{(5 x + 4) l n (7)} \cdot 5 ln (7)

e^{(5 x + 4) l n (7)} = 7^{5 x + 4}

= 5 ln (7) \cdot 7^{5 x + 4}

Graph

Beliebte Beispiele

integral of e^{-x}cos(4x)

\int e^{- x} cos (4 x) d x

limit as x approaches infinity of 5+6/x

x \to \infty lim (5 + \frac{6}{x})

2y^{''}-4y^'+8y=0

2 y^{^{''}} - 4 y^{^{'}} + 8 y = 0

\frac{d q}{d t} = k q^{2}

derivative of 21x+x^2

\frac{d}{d x} (21 x + x^{2})