derivative of 7^{x^2}

Lösung

\frac{d}{d x} (7^{x^{2}})

2 ln (7) \cdot 7^{x^{2}} x

Schritte zur Lösung

\frac{d}{d x} (7^{x^{2}})

Wende Exponentenregel an:

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

7^{x^{2}} = e^{x^{2} l n (7)}

= \frac{d}{d x} (e^{x^{2} l n (7)})

Wende die Kettenregel an:

e^{x^{2} l n (7)} \frac{d}{d x} (x^{2} ln (7))

= e^{x^{2} l n (7)} \frac{d}{d x} (x^{2} ln (7))

\frac{d}{d x} (x^{2} ln (7)) = 2 ln (7) x

= e^{x^{2} l n (7)} \cdot 2 ln (7) x

e^{x^{2} l n (7)} = 7^{x^{2}}

= 2 ln (7) \cdot 7^{x^{2}} x

\int - 3 x^{2} - 20 x + 2000 d x

(1 + x^{2}) \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

\int 3 x^{2} + 8 x - 9 d x

\frac{\partial}{\partial x} (ln (t + 2 c x))

d er i v a t i v e f (x) = a x^{b} + d e^{- c x}