derivative of (4x^2+5(5x-3))

Lösung

\frac{d}{d x} ((4 x^{2} + 5) (5 x - 3))

60 x^{2} - 24 x + 25

Schritte zur Lösung

\frac{d}{d x} ((4 x^{2} + 5) (5 x - 3))

Wende die Produktregel an:

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

f = 4 x^{2} + 5, g = 5 x - 3

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

\frac{d}{d x} (4 x^{2} + 5) = 8 x

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

= 8 x (5 x - 3) + 5 (4 x^{2} + 5)

Vereinfache

8 x (5 x - 3) + 5 (4 x^{2} + 5) : 60 x^{2} - 24 x + 25

= 60 x^{2} - 24 x + 25

x \to 90 lim (cos (x))

\int_{0}^{9} \frac{3}{3 x - 1} d x

d er i v a t i v e f (4) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 8 x

\frac{d ^{2}}{d x ^{2}} (sec (θ))

d er i v a t i v e - \frac{1}{x ^{3}}