derivative of (x^2+18(2x+15))

Lösung

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

6 x^{2} + 30 x + 36

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

Wende die Produktregel an:

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

f = x^{2} + 18, g = 2 x + 15

= \frac{d}{d x} (x^{2} + 18) (2 x + 15) + \frac{d}{d x} (2 x + 15) (x^{2} + 18)

\frac{d}{d x} (x^{2} + 18) = 2 x

\frac{d}{d x} (2 x + 15) = 2

= 2 x (2 x + 15) + 2 (x^{2} + 18)

Vereinfache

2 x (2 x + 15) + 2 (x^{2} + 18) : 6 x^{2} + 30 x + 36

= 6 x^{2} + 30 x + 36

d er i v a t i v e y = x^{3} (9 - x^{2})

d er i v a t i v e 2 x^{7} + 3 x + 11

1 + y^{2} + 2 (t + 1) y \frac{d y}{d t} = 0, y (0) = 1

x \frac{d y}{d x} + (1 - 3 x) y = e^{5 x}

f (x) = \frac{sin ( x )}{e ^{x}}