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

Lösung

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

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

\int 3^{2} d x

d er i v a t i v e f (x) = e^{\frac{z}{( z - 2 )}}

\int \frac{1}{( 3 x + 1 ) ^{4}} d x

\frac{\partial}{\partial x} (4 sin (x^{3} y^{2}))