derivative of 3e^x(5x^5-2)

Lösung

\frac{d}{d x} (3 e^{x} (5 x^{5} - 2))

3 (e^{x} (5 x^{5} - 2) + 25 x^{4} e^{x})

Schritte zur Lösung

\frac{d}{d x} (3 e^{x} (5 x^{5} - 2))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (e^{x} (5 x^{5} - 2))

Wende die Produktregel an:

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

f = e^{x}, g = 5 x^{5} - 2

= 3 (\frac{d}{d x} (e^{x}) (5 x^{5} - 2) + \frac{d}{d x} (5 x^{5} - 2) e^{x})

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

\frac{d}{d x} (5 x^{5} - 2) = 25 x^{4}

= 3 (e^{x} (5 x^{5} - 2) + 25 x^{4} e^{x})

y^{'} = sin^{2} (x - y)

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

\frac{d}{d x} (5 e^{x})

\frac{\partial}{\partial x} ((3 x^{2} + 3 x - 1) (2 x + 3))

d er i v a t i v e y = (x + 5) (3 x + 8)