derivative of x^2sqrt(3x+1)

Lösung

\frac{d}{d x} (x^{2} 3 x + 1)

\frac{15 x ^{2} + 4 x}{2 3 x + 1}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 3 x + 1)

Wende die Produktregel an:

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

f = x^{2}, g = 3 x + 1

= \frac{d}{d x} (x^{2}) 3 x + 1 + \frac{d}{d x} (3 x + 1) x^{2}

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

\frac{d}{d x} (3 x + 1) = \frac{3}{2 3 x + 1}

= 2 x 3 x + 1 + \frac{3}{2 3 x + 1} x^{2}

Vereinfache

2 x 3 x + 1 + \frac{3}{2 3 x + 1} x^{2} : \frac{15 x ^{2} + 4 x}{2 3 x + 1}

= \frac{15 x ^{2} + 4 x}{2 3 x + 1}

\int \frac{x}{y ^{2} + x ^{2}} d x

x \to 1 lim (\frac{x ^{3} - 1}{x - 6})

d er i v a t i v e x^{e}

\int \frac{2 ^{x}}{x} d x

\int \frac{x ^{2}}{( x ^{3} - 3 ) ^{2}} d x