derivative of in(3x+1(x+2)2)

Lösung

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

i (14 n + 12 n x)

Schritte zur Lösung

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

Vereinfache

in (3 x + 1) (x + 2) \cdot 2 : i (4 n + 14 n x + 6 n x^{2})

= \frac{d}{d x} (i (4 n + 14 n x + 6 n x^{2}))

Entferne die Konstante:

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

= i \frac{d}{d x} (4 n + 14 n x + 6 n x^{2})

Wende die Summen-/Differenzregel an:

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

= i (\frac{d}{d x} (4 n) + \frac{d}{d x} (14 n x) + \frac{d}{d x} (6 n x^{2}))

\frac{d}{d x} (4 n) = 0

\frac{d}{d x} (14 n x) = 14 n

\frac{d}{d x} (6 n x^{2}) = 12 n x

= i (0 + 14 n + 12 n x)

Vereinfache

i (0 + 14 n + 12 n x) : i (14 n + 12 n x)

= i (14 n + 12 n x)

f a c t or a x^{n} + b x^{n - 1}

\int 2 x^{3} - 6 x^{2} d x

\frac{d y}{d x} + y = \frac{1 - e ^{- 2 x}}{e ^{x} + e ^{- x}}

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

f (x) = \frac{cos ( t )}{t ^{7}}