derivative of 3*4^{x^2+2}

Lösung

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

3 ln (2) \cdot 2^{2 x^{2} + 6} x

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

4^{x^{2} + 2} = e^{(x^{2} + 2) l n (4)}

= 3 \frac{d}{d x} (e^{(x^{2} + 2) l n (4)})

Wende die Kettenregel an:

e^{(x^{2} + 2) l n (4)} \frac{d}{d x} ((x^{2} + 2) ln (4))

= e^{(x^{2} + 2) l n (4)} \frac{d}{d x} ((x^{2} + 2) ln (4))

\frac{d}{d x} ((x^{2} + 2) ln (4)) = 4 ln (2) x

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

Vereinfache

3 e^{(x^{2} + 2) l n (4)} \cdot 4 ln (2) x : 3 ln (2) \cdot 2^{2 x^{2} + 6} x

= 3 ln (2) \cdot 2^{2 x^{2} + 6} x

\int \frac{1}{( x + 1 ) ^{2} + 25} d x

\int_{1}^{3} x e^{x^{2}} d x

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

a re a y = 6 - 6 x, y = 0, x = 0

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