derivative 3t(2t^2-5)^4

Lösung

ableitung von

3 t (2 t^{2} - 5)^{4}

3 ((2 t^{2} - 5)^{4} + 16 t^{2} (2 t^{2} - 5)^{3})

Schritte zur Lösung

\frac{d}{d t} (3 t (2 t^{2} - 5)^{4})

Entferne die Konstante:

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

= 3 \frac{d}{d t} (t (2 t^{2} - 5)^{4})

Wende die Produktregel an:

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

f = t, g = (2 t^{2} - 5)^{4}

= 3 (\frac{d t}{d t} (2 t^{2} - 5)^{4} + \frac{d}{d t} ((2 t^{2} - 5)^{4}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((2 t^{2} - 5)^{4}) = 16 t (2 t^{2} - 5)^{3}

= 3 (1 \cdot (2 t^{2} - 5)^{4} + 16 t (2 t^{2} - 5)^{3} t)

Vereinfache

3 (1 \cdot (2 t^{2} - 5)^{4} + 16 t (2 t^{2} - 5)^{3} t) : 3 ((2 t^{2} - 5)^{4} + 16 t^{2} (2 t^{2} - 5)^{3})

= 3 ((2 t^{2} - 5)^{4} + 16 t^{2} (2 t^{2} - 5)^{3})

in v erse l a pl a ce \frac{( s - 2 )}{( s - 2 ) ^{2} + 1}

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

t an g e n t f (x) = 7 x - 6 x, at x = 1

x \to 10 lim (12 x)

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