de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

2 (x^{3} + 5 x) (3 x^{2} + 5) (5 x - 3)^{4} + 20 (5 x - 3)^{3} (x^{3} + 5 x)^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((5 x - 3)^{4}) = 20 (5 x - 3)^{3}

= 2 (x^{3} + 5 x) (3 x^{2} + 5) (5 x - 3)^{4} + 20 (5 x - 3)^{3} (x^{3} + 5 x)^{2}

Graph

Beliebte Beispiele

f (x) = tan (7 x)

integral of 1/(x(x^3+1)^2)

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

derivative e^{7tsin(2t)}

d er i v a t i v e e^{7 t s i n (2 t)}

tangent f(x)=(-2x)/(x^2+1),\at x=1

t an g e n t f (x) = \frac{- 2 x}{x ^{2} + 1}, at x = 1

integral of 2/((x+1)^2)

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