derivative x^2sqrt(3x+5)

Lösung

ableitung von

x^{2} 3 x + 5

\frac{15 x ^{2} + 20 x}{2 3 x + 5}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 x 3 x + 5 + \frac{3}{2 3 x + 5} x^{2}

Vereinfache

2 x 3 x + 5 + \frac{3}{2 3 x + 5} x^{2} : \frac{15 x ^{2} + 20 x}{2 3 x + 5}

= \frac{15 x ^{2} + 20 x}{2 3 x + 5}

\int \frac{x}{( x ^{2} + 7 ) ^{2}} d x

d er i v a t i v e f (x) = (- 3 x^{3} + 3 x^{2})^{3}

x \to - 1 lim (arccos (x))

\int_{0}^{π} 3 sin^{2} (x co) s^{4} x d x

x \to 7 lim (\frac{( \frac{1}{x} - \frac{1}{7} )}{x - 7})