derivative of 4x^2*2^{(3x+1})

Lösung

\frac{d}{d x} (4 x^{2} \cdot 2^{(3 x + 1)})

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

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} \cdot 2^{(3 x + 1)})

Vereinfache

4 x^{2} \cdot 2^{(3 x + 1)} : 2^{3 x + 3} x^{2}

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

Wende die Produktregel an:

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

f = 2^{3 x + 3}, g = x^{2}

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

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

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

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

2 x \cdot 2^{3 x + 3} = 2^{3 x + 4} x

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

((x + 30) 3 2 - x)^{^{'}}

\frac{\partial}{\partial x} ((x^{2} + y^{2}) e^{y^{2} - x^{2}})

x \to 3 + lim (4)

\int \frac{3}{5 x ^{3}} d x

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