derivative of 3^{2x^2}*sqrt(x)

Lösung

\frac{d}{d x} (3^{2 x^{2}} \cdot x)

4 ln (3) \cdot 9^{x^{2}} x x + \frac{9 ^{x^{2}}}{2 x}

Schritte zur Lösung

\frac{d}{d x} (3^{2 x^{2}} x)

Vereinfache

3^{2 x^{2}} x : 9^{x^{2}} x

= \frac{d}{d x} (9^{x^{2}} x)

Wende die Produktregel an:

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

f = 9^{x^{2}}, g = x

= \frac{d}{d x} (9^{x^{2}}) x + \frac{d}{d x} (x) 9^{x^{2}}

\frac{d}{d x} (9^{x^{2}}) = 4 ln (3) \cdot 9^{x^{2}} x

\frac{d}{d x} (x) = \frac{1}{2 x}

= 4 ln (3) \cdot 9^{x^{2}} x x + \frac{1}{2 x} \cdot 9^{x^{2}}

\frac{1}{2 x} \cdot 9^{x^{2}} = \frac{9 ^{x^{2}}}{2 x}

= 4 ln (3) \cdot 9^{x^{2}} x x + \frac{9 ^{x^{2}}}{2 x}

\frac{d}{d x} (\frac{10}{x ^{2} + 1})

x \to - 4 lim (\frac{1}{2} x - 1)

d er i v a t i v e \frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}}

d er i v a t i v e y = 5 cos^{2} (π x)

\frac{d}{d x} (ln (2 x + 3 y))