derivative 4x^3+e^{16x}-3^{2x-1}

Lösung

ableitung von

4 x^{3} + e^{16 x} - 3^{2 x - 1}

12 x^{2} + e^{16 x} \cdot 16 - 2 ln (3) \cdot 3^{2 x - 1}

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} + e^{16 x} - 3^{2 x - 1})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (e^{16 x}) - \frac{d}{d x} (3^{2 x - 1})

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (e^{16 x}) = e^{16 x} \cdot 16

\frac{d}{d x} (3^{2 x - 1}) = 2 ln (3) \cdot 3^{2 x - 1}

= 12 x^{2} + e^{16 x} \cdot 16 - 2 ln (3) \cdot 3^{2 x - 1}

\int (\frac{x ^{3}}{1 - x ^{2}}) d x

\int 4 3 y + 1 d y

ma c l a u r in - x^{4} + 2 x^{3} - 5 x^{2} + 0.4

\int_{1}^{4} 3 x d x

in v erse l a pl a ce \frac{s + 5}{s ( s + 10 ) ^{2}}