derivative of (2x^2+1^{3/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x^{2} + 1) = 4 x

= \frac{3 ( 2 x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 4 x

Vereinfache

\frac{3 ( 2 x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \cdot 4 x : 6 x (2 x^{2} + 1)^{\frac{1}{2}}

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

\int_{- 2}^{1} (8 x^{3} - 3 x^{2}) d x

\frac{d y}{d x} = 3 x e^{y}

t an g e n t (7 - 6 x)^{\frac{1}{2}}, at x = - 1

\int_{1}^{2} \frac{1}{x ^{3}} d x

t an g e n t f (x) = x^{2} + x, (2, 6)