derivative x^pipi^x

Lösung

ableitung von

x^{π} π^{x}

π^{1 + x} x^{π - 1} + ln (π) π^{x} x^{π}

Schritte zur Lösung

\frac{d}{d x} (x^{π} π^{x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{π}, g = π^{x}

= \frac{d}{d x} (x^{π}) π^{x} + \frac{d}{d x} (π^{x}) x^{π}

\frac{d}{d x} (x^{π}) = π x^{π - 1}

\frac{d}{d x} (π^{x}) = π^{x} ln (π)

= π x^{π - 1} π^{x} + π^{x} ln (π) x^{π}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

π π^{x} = π^{1 + x}

= π^{1 + x} x^{π - 1} + ln (π) π^{x} x^{π}

d er i v a t i v e f (x) = 4 x^{\frac{3}{5}}

\int_{- 9}^{9} 58

x \to 0 lim (\frac{x + 3}{x})

\int (sin^{2} (x) + cos^{2} (x)) d x

t an g e n t x^{2} + x y - y^{2} = - 1, (3, 5)