derivative g(x)=(x-4)^3+3x(x-4)^2

Lösung

ableitung von

g (x) = (x - 4)^{3} + 3 x (x - 4)^{2}

12 x^{2} - 72 x + 96

Schritte zur Lösung

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

Vereinfache

(x - 4)^{3} + 3 x (x - 4)^{2} : 4 x^{3} - 36 x^{2} + 96 x - 64

= \frac{d}{d x} (4 x^{3} - 36 x^{2} + 96 x - 64)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (96 x) - \frac{d}{d x} (64)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (96 x) = 96

\frac{d}{d x} (64) = 0

= 12 x^{2} - 72 x + 96 - 0

Vereinfache

= 12 x^{2} - 72 x + 96

\frac{\partial}{\partial x} (x y e^{- 9 y})

in v erse l a pl a ce \frac{a}{s}

\int_{2}^{6} 7 x^{3} d x

\frac{\partial}{\partial y} (5 x y - 10 y)

\int \frac{1}{t + 1} d t