derivative of e^{x^4}*4x^3

Lösung

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

4 (4 e^{x^{4}} x^{6} + 3 e^{x^{4}} x^{2})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = e^{x^{4}}, g = x^{3}

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

\frac{d}{d x} (e^{x^{4}}) = e^{x^{4}} \cdot 4 x^{3}

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

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

e^{x^{4}} \cdot 4 x^{3} x^{3} = 4 e^{x^{4}} x^{6}

= 4 (4 e^{x^{4}} x^{6} + 3 e^{x^{4}} x^{2})

x^{^{''}} + k x = 0

\frac{d y}{d x} = 10 - \frac{2 y}{100 - x}

t an g e n t f (x) = 3 x^{2} - 5, at x = 2

x \to 3 π + lim (cot (x))

\frac{\partial}{\partial x} (ln (\frac{x y}{y + z}))