derivative-3x(5x+4)^6

Lösung

ableitung von

- 3 x (5 x + 4)^{6}

- 3 ((5 x + 4)^{6} + 30 x (5 x + 4)^{5})

Schritte zur Lösung

\frac{d}{d x} (- 3 x (5 x + 4)^{6})

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (x (5 x + 4)^{6})

Wende die Produktregel an:

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

f = x, g = (5 x + 4)^{6}

= - 3 (\frac{d x}{d x} (5 x + 4)^{6} + \frac{d}{d x} ((5 x + 4)^{6}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((5 x + 4)^{6}) = 30 (5 x + 4)^{5}

= - 3 (1 \cdot (5 x + 4)^{6} + 30 (5 x + 4)^{5} x)

Vereinfache

= - 3 ((5 x + 4)^{6} + 30 x (5 x + 4)^{5})

\int 13 x d x

f (t) = e^{6 t s i n (2 t)}

y^{^{''}} - 8 y^{^{'}} - 9 y = 0

x \to 3 - lim (\frac{x - 3}{x - 3})

\int \frac{3}{x ^{2} - 8 x + 25} d x