derivative y=3(x^2-x+1)(5x-3)

Lösung

ableitung von

y = 3 (x^{2} - x + 1) (5 x - 3)

3 (15 x^{2} - 16 x + 8)

Schritte zur Lösung

\frac{d}{d x} (3 (x^{2} - x + 1) (5 x - 3))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} ((x^{2} - x + 1) (5 x - 3))

Wende die Produktregel an:

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

f = x^{2} - x + 1, g = 5 x - 3

= 3 (\frac{d}{d x} (x^{2} - x + 1) (5 x - 3) + \frac{d}{d x} (5 x - 3) (x^{2} - x + 1))

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

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

= 3 ((2 x - 1) (5 x - 3) + 5 (x^{2} - x + 1))

Multipliziere aus

(2 x - 1) (5 x - 3) + 5 (x^{2} - x + 1) : 15 x^{2} - 16 x + 8

= 3 (15 x^{2} - 16 x + 8)

\frac{\partial}{\partial x} ((x + y^{2})^{3})

t an g e n t \frac{4}{x}, at x = - 5

\int 5 x cos (3 x) d x

\int \frac{1}{( 4 x ^{2} - 4 x - 3 ) ^{\frac{3}{2}}} d x

d er i v a t i v e 4 + 0.45 \cdot sin (\frac{2 π t}{3.7})