derivative of (2x^2+5(5x-3))

Lösung

\frac{d}{d x} ((2 x^{2} + 5) (5 x - 3))

30 x^{2} - 12 x + 25

Schritte zur Lösung

\frac{d}{d x} ((2 x^{2} + 5) (5 x - 3))

Wende die Produktregel an:

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

f = 2 x^{2} + 5, g = 5 x - 3

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

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

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

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

Vereinfache

4 x (5 x - 3) + 5 (2 x^{2} + 5) : 30 x^{2} - 12 x + 25

= 30 x^{2} - 12 x + 25

\frac{d y}{d x} = \frac{x + y}{y - x}

t an g e n t f (x) = 10 x^{3} - 45 x^{2} + 60 x - 30

a re a y = e^{2 x}, x = 0, x = 3

\int \frac{e ^{6 t}}{t} d t

\frac{d}{d x} (e^{(\frac{- k}{x})})