derivative of (5x^3+8x-3^{3/2})

Lösung

\frac{d}{d x} ((5 x^{3} + 8 x - 3)^{\frac{3}{2}})

\frac{3 ( 15 x ^{2} + 8 ) ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{3} + 8 x - 3)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{3} + 8 x - 3)

= \frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (5 x^{3} + 8 x - 3)

\frac{d}{d x} (5 x^{3} + 8 x - 3) = 15 x^{2} + 8

= \frac{3 ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2} (15 x^{2} + 8)

Multipliziere Brüche:

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

= \frac{3 ( 15 x ^{2} + 8 ) ( 5 x ^{3} + 8 x - 3 ) ^{\frac{1}{2}}}{2}

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

3 \frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + y = 0

t an g e n t 5 x - 2 x

y^{^{'}} = 5 y sin (4 x), y (\frac{π}{8}) = 3

n = 1 \sum \infty \frac{1}{π ^{n}}