derivative of (9sqrt(x)+4x^2)

Lösung

\frac{d}{d x} ((9 x + 4) x^{2})

\frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 4)

Schritte zur Lösung

\frac{d}{d x} ((9 x + 4) x^{2})

Wende die Produktregel an:

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

f = 9 x + 4, g = x^{2}

= \frac{d}{d x} (9 x + 4) x^{2} + \frac{d}{d x} (x^{2}) (9 x + 4)

\frac{d}{d x} (9 x + 4) = \frac{9}{2 x}

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

= \frac{9}{2 x} x^{2} + 2 x (9 x + 4)

\frac{9}{2 x} x^{2} = \frac{9 x ^{\frac{3}{2}}}{2}

= \frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 4)

(40 q^{2} + q + 500)^{^{'}}

x \to - 1 + lim (\frac{3}{x + 1})

d er i v a t i v e y = e^{x} + 1

x \to 0 lim (e^{- x} x^{2})

\int_{0}^{1} e^{- 0.1 x} d x