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

Lösung

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

6 x^{5} + 8 x^{3} + 2 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} + 2, g = x^{4} + 1

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

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

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

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

Vereinfache

2 x (x^{4} + 1) + 4 x^{3} (x^{2} + 2) : 6 x^{5} + 8 x^{3} + 2 x

= 6 x^{5} + 8 x^{3} + 2 x

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

\int \frac{1}{4 ( x + 1 )} d x

\int_{0}^{π} x cos (x^{2}) d x

y^{^{'}} = (2 y + 22)^{0.5}

d er i v a t i v e f (x) = (x^{3} + 1) \cdot 3 x^{2}