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

Lösung

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

6 x^{2} (x^{3} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{3} + 2)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((x^{3} + 2)^{2}) = 6 x^{2} (x^{3} + 2)

\frac{d}{d x} ((x^{4} + 4)^{4}) = 16 x^{3} (x^{4} + 4)^{3}

= 6 x^{2} (x^{3} + 2) (x^{4} + 4)^{4} + 16 x^{3} (x^{4} + 4)^{3} (x^{3} + 2)^{2}

y^{^{'}} (t) = 0.3 y \cdot (1 - \frac{y}{2500}) - \frac{y}{4}, y (0) = 600

\frac{\partial}{\partial x} (cos (- 5 x - 6 y))

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

l a pl a ce t r an s f or m t^{2} + t + 1

\int \frac{25}{x} d x