derivative (2x+5)^3(x^5+3)^6

Lösung

ableitung von

(2 x + 5)^{3} (x^{5} + 3)^{6}

6 (2 x + 5)^{2} (x^{5} + 3)^{6} + 30 x^{4} (x^{5} + 3)^{5} (2 x + 5)^{3}

Schritte zur Lösung

\frac{d}{d x} ((2 x + 5)^{3} (x^{5} + 3)^{6})

Wende die Produktregel an:

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

f = (2 x + 5)^{3}, g = (x^{5} + 3)^{6}

= \frac{d}{d x} ((2 x + 5)^{3}) (x^{5} + 3)^{6} + \frac{d}{d x} ((x^{5} + 3)^{6}) (2 x + 5)^{3}

\frac{d}{d x} ((2 x + 5)^{3}) = 6 (2 x + 5)^{2}

\frac{d}{d x} ((x^{5} + 3)^{6}) = 30 x^{4} (x^{5} + 3)^{5}

= 6 (2 x + 5)^{2} (x^{5} + 3)^{6} + 30 x^{4} (x^{5} + 3)^{5} (2 x + 5)^{3}

\int \frac{16 x}{1 - x ^{4}} d x

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

\frac{d y}{d x} = 8 x e^{7 y}

\int \frac{- 7}{x ^{2} + 16} d x

x \to 5 lim (\frac{( ln ( \frac{x}{5} ) )}{x ^{2} - 25})