derivative of (7^{10x+1})

Lösung

\frac{d}{d x} ((7)^{10 x + 1})

10 ln (7) \cdot 7^{10 x + 1}

Schritte zur Lösung

\frac{d}{d x} ((7)^{10 x + 1})

Wende Exponentenregel an:

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

7^{10 x + 1} = e^{(10 x + 1) l n (7)}

= \frac{d}{d x} (e^{(10 x + 1) l n (7)})

Wende die Kettenregel an:

e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

= e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

\frac{d}{d x} ((10 x + 1) ln (7)) = 10 ln (7)

= e^{(10 x + 1) l n (7)} \cdot 10 ln (7)

e^{(10 x + 1) l n (7)} = 7^{10 x + 1}

= 10 ln (7) \cdot 7^{10 x + 1}

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

\int \frac{2 x + 1}{x ^{2} + 2 x + 37} d x

\frac{d}{d x} (sin (x) \cdot sin (x))

\int_{- 9}^{9} 81 - x^{2} d x

t y^{^{'}} - 2 y = t^{5} sin (2 t) - t^{3} + 4 t^{4}