derivative of ({f}(x)(2x^3-15x^2+24x+19))

Lösung

\frac{d}{d x} ((f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19))

\frac{d}{d x} (f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19) + (6 x^{2} - 30 x + 24) f (x)

Schritte zur Lösung

\frac{d}{d x} ((f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19))

Wende die Produktregel an:

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

f = f (x), g = 2 x^{3} - 15 x^{2} + 24 x + 19

= \frac{d}{d x} (f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19) + \frac{d}{d x} (2 x^{3} - 15 x^{2} + 24 x + 19) f (x)

\frac{d}{d x} (2 x^{3} - 15 x^{2} + 24 x + 19) = 6 x^{2} - 30 x + 24

= \frac{d}{d x} (f (x)) (2 x^{3} - 15 x^{2} + 24 x + 19) + (6 x^{2} - 30 x + 24) f (x)

e x p an d (x + 2)^{3} - e^{3 x}

e x p an d 2 x y d x + (x^{2} - 1) d y

s im pl i f y (sin (x) - cos (x)) (cos (x) - sin (x))

e x p an d (3 x - 3)^{4}

e x p an d \frac{0.1 ( s + 1 ) ( s + 30.1 )}{s}