derivative y=(4x^3+5)(x^4-3x)

Lösung

ableitung von

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

28 x^{6} - 28 x^{3} - 15

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 4 x^{3} + 5, g = x^{4} - 3 x

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

\frac{d}{d x} (4 x^{3} + 5) = 12 x^{2}

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

= 12 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (4 x^{3} + 5)

Vereinfache

12 x^{2} (x^{4} - 3 x) + (4 x^{3} - 3) (4 x^{3} + 5) : 28 x^{6} - 28 x^{3} - 15

= 28 x^{6} - 28 x^{3} - 15

n = 1 \sum \infty n + \frac{1}{n ^{2}}

\frac{d y}{d x} = 2 x

\int_{1}^{5} π (x - 1) d x

\int \frac{( y + 1 ) ^{2}}{y} d y

d er i v a t i v e 2 - x^{2}