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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

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

\int \frac{cos ( \frac{π}{x ^{9}} )}{x ^{10}} d x

\int_{1}^{2} t t - 1 d t

x \to c lim (\frac{27}{18})

\frac{\partial}{\partial x} (\frac{( 3 x + 8 )}{4 y + 1})

\int_{0}^{1} (6 x + 1) d x