derivative f(x)=sqrt((5-2x)(3x-1)^3)

Lösung

ableitung von

f (x) = (5 - 2 x) (3 x - 1)^{3}

\frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} ((5 - 2 x) (3 x - 1)^{3}) = - 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x)

= \frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} (- 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x))

Vereinfache

\frac{1}{2 ( 5 - 2 x ) ( 3 x - 1 ) ^{3}} (- 2 (3 x - 1)^{3} + 9 (3 x - 1)^{2} (5 - 2 x)) : \frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}

= \frac{( - 24 x + 47 ) ( 3 x - 1 ) ^{\frac{3}{2}}}{2 ( 3 x - 1 ) ^{2} - 2 x + 5}

\int \frac{x + 3}{3 x ^{2} - 6 x + 8} d x

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\int_{1}^{3} (x^{2} + 2 x - 4) d x

n = 1 \sum \infty \frac{5 ^{n}}{3 ^{n}}

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