derivative 9(x^2+5x)^2(2x+5)

Lösung

ableitung von

9 (x^{2} + 5 x)^{2} (2 x + 5)

9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)

Schritte zur Lösung

\frac{d}{d x} (9 (x^{2} + 5 x)^{2} (2 x + 5))

Entferne die Konstante:

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

= 9 \frac{d}{d x} ((x^{2} + 5 x)^{2} (2 x + 5))

Wende die Produktregel an:

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

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

= 9 (\frac{d}{d x} ((x^{2} + 5 x)^{2}) (2 x + 5) + \frac{d}{d x} (2 x + 5) (x^{2} + 5 x)^{2})

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

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

= 9 (2 (x^{2} + 5 x) (2 x + 5) (2 x + 5) + 2 (x^{2} + 5 x)^{2})

Vereinfache

9 (2 (x^{2} + 5 x) (2 x + 5) (2 x + 5) + 2 (x^{2} + 5 x)^{2}) : 9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)

= 9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)

d er i v a t i v e (7^{x})^{4}

d er i v a t i v e y (θ) = e tan (θ)

\frac{d y}{d x} - 3 y = - 6

f (x) = (x + \frac{1}{3 x})^{2}

ma c l a u r in ln (1 + 5 x)