derivative of (3x^3+1(-4x^2-3)^4)

Lösung

\frac{d}{d x} ((3 x^{3} + 1) (- 4 x^{2} - 3)^{4})

9 x^{2} (- 4 x^{2} - 3)^{4} - 32 x (- 4 x^{2} - 3)^{3} (3 x^{3} + 1)

Schritte zur Lösung

\frac{d}{d x} ((3 x^{3} + 1) (- 4 x^{2} - 3)^{4})

Wende die Produktregel an:

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

f = 3 x^{3} + 1, g = (- 4 x^{2} - 3)^{4}

= \frac{d}{d x} (3 x^{3} + 1) (- 4 x^{2} - 3)^{4} + \frac{d}{d x} ((- 4 x^{2} - 3)^{4}) (3 x^{3} + 1)

\frac{d}{d x} (3 x^{3} + 1) = 9 x^{2}

\frac{d}{d x} ((- 4 x^{2} - 3)^{4}) = - 32 x (- 4 x^{2} - 3)^{3}

= 9 x^{2} (- 4 x^{2} - 3)^{4} + (- 32 x (- 4 x^{2} - 3)^{3}) (3 x^{3} + 1)

Vereinfache

= 9 x^{2} (- 4 x^{2} - 3)^{4} - 32 x (- 4 x^{2} - 3)^{3} (3 x^{3} + 1)

x \to 4 lim (\frac{x ^{2} - 6}{x - 4})

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

d er i v a t i v e 14 \cdot (\frac{- x + 2}{x ^{2}})

\int e^{3 y} d y

l a pl a ce t r an s f or m e^{- 3 t} sin (t)