derivative f(x)=2*7^{2x^2+3}

Lösung

ableitung von

f (x) = 2 \cdot 7^{2 x^{2} + 3}

8 ln (7) \cdot 7^{2 x^{2} + 3} x

Schritte zur Lösung

\frac{d}{d x} (2 \cdot 7^{2 x^{2} + 3})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (7^{2 x^{2} + 3})

Wende Exponentenregel an:

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

7^{2 x^{2} + 3} = e^{(2 x^{2} + 3) l n (7)}

= 2 \frac{d}{d x} (e^{(2 x^{2} + 3) l n (7)})

Wende die Kettenregel an:

e^{(2 x^{2} + 3) l n (7)} \frac{d}{d x} ((2 x^{2} + 3) ln (7))

= e^{(2 x^{2} + 3) l n (7)} \frac{d}{d x} ((2 x^{2} + 3) ln (7))

\frac{d}{d x} ((2 x^{2} + 3) ln (7)) = 4 ln (7) x

= 2 e^{(2 x^{2} + 3) l n (7)} \cdot 4 ln (7) x

Vereinfache

2 e^{(2 x^{2} + 3) l n (7)} \cdot 4 ln (7) x : 8 ln (7) \cdot 7^{2 x^{2} + 3} x

= 8 ln (7) \cdot 7^{2 x^{2} + 3} x

\int \frac{( x ^{3} )}{x ^{2} + 25} d x

\frac{\partial}{\partial t} (s cos (t))

t a y l or x - x^{3}, - 2

\frac{\partial}{\partial y} (3 x z^{2} e^{y^{2}})

d er i v a t i v e f (x) = \frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}