derivative of x^{15x}

Lösung

\frac{d}{d x} (x^{15 x})

15 x^{15 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{15 x})

Wende Exponentenregel an:

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

x^{15 x} = e^{15 x l n (x)}

= \frac{d}{d x} (e^{15 x l n (x)})

Wende die Kettenregel an:

e^{15 x l n (x)} \frac{d}{d x} (15 x ln (x))

= e^{15 x l n (x)} \frac{d}{d x} (15 x ln (x))

\frac{d}{d x} (15 x ln (x)) = 15 (ln (x) + 1)

= e^{15 x l n (x)} \cdot 15 (ln (x) + 1)

e^{15 x l n (x)} = x^{15 x}

= 15 x^{15 x} (ln (x) + 1)

\int \frac{6 x}{( x - 5 ) ^{2}} d x

x \to 2 lim (6 x^{2} + 1)

\int_{- \infty}^{0} e^{9 x} d x

t^{2} (\frac{d y}{d t}) + 4 t y - y^{3} = 0

s l o p e x^{3} + y^{3} - 6 x y = 0, (\frac{4}{3}, \frac{8}{3})