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Beliebt Rechnen >

derivative of (6x+5^x)

Lösung

\frac{d}{d x} ((6 x + 5)^{x})

Lösung

(ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

Schritte zur Lösung

\frac{d}{d x} ((6 x + 5)^{x})

Wende Exponentenregel an:

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

(6 x + 5)^{x} = e^{x l n (6 x + 5)}

= \frac{d}{d x} (e^{x l n (6 x + 5)})

Wende die Kettenregel an:

e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

= e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

\frac{d}{d x} (x ln (6 x + 5)) = ln (6 x + 5) + \frac{6 x}{6 x + 5}

= e^{x l n (6 x + 5)} (ln (6 x + 5) + \frac{6 x}{6 x + 5})

e^{x l n (6 x + 5)} = (6 x + 5)^{x}

= (ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

Graph

Beliebte Beispiele

sum from n=0 to infinity of (x^n)/(2n!)

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

taylor e^{(-x/2)},0

t a y l or e^{(- \frac{x}{2})}, 0

derivative of e^xsin(5x)

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

derivative of 100x^{3/4}y^{1/4}

\frac{d}{d x} (100 x^{\frac{3}{4}} y^{\frac{1}{4}})

steigung (-2,0),(0,-4)

s l o p e (- 2, 0), (0, - 4)