(\partial)/(\partial x)((3x^2+5x+1)^{3/2})

Lösung

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

\frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

Schritte zur Lösung

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

\frac{\partial}{\partial x} (3 x^{2} + 5 x + 1) = 6 x + 5

= \frac{3 ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2} (6 x + 5)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( 6 x + 5 ) ( 3 x ^{2} + 5 x + 1 ) ^{\frac{1}{2}}}{2}

\int x \cdot \frac{5}{2} \cdot x^{2} + 7 d x

\int_{0}^{2} 2^{- x} d x

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y})

x \to 0 lim (2 (1 + 3 x)^{\frac{2}{x}})

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