derivative y=(9sqrt(x)+5)x^2

Lösung

ableitung von

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

\frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 9 x + 5, g = x^{2}

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

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

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

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

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

= \frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)

n = 1 \sum \infty \frac{1 ^{n}}{n + 2}

x \to 2 - lim (c x^{2} + 6 x)

\int \frac{x ^{2} + 32 x - 16}{x ^{3} - 16 x} d x

\int (- 3 x + 4) d x

\frac{\partial}{\partial x} ((y + z) (arcsin (x)))