derivative of 5x^3+7x^{2.5}-3x+1

Lösung

\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

15 x^{2} + 17.5 x^{1.5} - 3

Schritte zur Lösung

\frac{d}{d x} (5 x^{3} + 7 x^{2.5} - 3 x + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{3}) + \frac{d}{d x} (7 x^{2.5}) - \frac{d}{d x} (3 x) + \frac{d}{d x} (1)

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

\frac{d}{d x} (7 x^{2.5}) = 17.5 x^{1.5}

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (1) = 0

= 15 x^{2} + 17.5 x^{1.5} - 3 + 0

Vereinfache

= 15 x^{2} + 17.5 x^{1.5} - 3

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

\frac{\partial}{\partial y} (5 x y)

ln (x) \frac{d y}{d x} = \frac{y}{x}

\frac{\partial}{\partial y} (e^{x} + x cos (y))

25 y^{^{''}} - 4 y = 0