derivative h(x)=2x(6x-18)^6

Lösung

ableitung von

h (x) = 2 x (6 x - 18)^{6}

2 ((6 x - 18)^{6} + 36 x (6 x - 18)^{5})

Schritte zur Lösung

\frac{d}{d x} (2 x (6 x - 18)^{6})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x (6 x - 18)^{6})

Wende die Produktregel an:

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

f = x, g = (6 x - 18)^{6}

= 2 (\frac{d x}{d x} (6 x - 18)^{6} + \frac{d}{d x} ((6 x - 18)^{6}) x)

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

\frac{d}{d x} ((6 x - 18)^{6}) = 36 (6 x - 18)^{5}

= 2 (1 \cdot (6 x - 18)^{6} + 36 (6 x - 18)^{5} x)

Vereinfache

= 2 ((6 x - 18)^{6} + 36 x (6 x - 18)^{5})

\int \frac{7 - 4 x ^{3} + 6 x ^{6}}{x ^{6}} d x

3 y^{^{''}} - 8 y^{^{'}} - 3 y = 0, y (0) = - 9, y^{^{'}} (0) = 8

\int_{1}^{3} (\frac{3 x ^{2} - 7}{x ^{3}}) d x

\int t^{3} (7 + t^{4})^{3} d t

x \to 1 lim ((x)^{\frac{1}{x - 1}})